Quite right, the cooking thermometer is the one element that can't be improvised. It's non-intuitive yet essential in these scenarios.

But of all the options you mention, which have you personally found, in practice, to be the most effective?

There are definitely ways to improvise a thermal cooker, but for the cost of buying one ahead of time...? We use ours on a routine basis, it’s not something that sits on a shelf unloved and forgotten until that very rare emergency.

FWIW, the outer insulation container (the jacket) has a stainless steel inner liner that fits the food pot (~5 quarts) that goes on the stove. Other brands are similar, some bigger some smaller. The stainless steel liner allows the jacket to be preheated with boiling water so that when the hot pot with the food is inserted, the jacket liner is already very hot and doesn’t take heat from the pot to warm up. 6 hours later it’s still hot.

I worry about our hot tub. Even at zero degrees outside, ours supposedly won't start freezing for a week or more (I'm not sure I believe that though). We could drain it, but then the back yard would turn into one gigantic ice rink. Unless you have a really big generator, backup power is not an option. 220v at 50amps is what the tub uses when the heaters and pumps are going, and you can't heat without the pumps running too (pumps don't have to be at full power though).

Another recommendation I've heard is a 120v submersible sump pump on a small generator with both the pump inlet and outlet under water. The heat of the motor supposedly keeps the tub from freezing. That would circulate water in the main body of the tub, but I am more worried about the plumbing lines freezing. A sump pump wouldn't circulate through the plumbing. I guess I'd try the sump pump, but if that appeared to not be working, raise the outlet and use the pump to quickly drain the tub. And just deal with the resulting skating rink.

I'd be interested to hear what other tub owners plan to do during extended power outages.

OK, we've moved from cooking with no power, to heating a house with no power, to maintaining a hot tub with no power. In a normal situation where we know the power will eventually come back, cooking would be my least concern. But at the end of the world when power would not be coming back, the hot tub would take last place in the concern department.

to add to CJK's comments on coolers, and for the members not familiar with the 2004 Florida storm season... we had 3 storms in a month's period or so... the first for me was a 9 day power outage, and the others 3 or 4 day events...at the time I had a 5 day rated cooler, an older Igloo, and a small cooler I used for ice at school for science labs...and no generator

I pre chilled the 5 day with a couple of frozen gallon jugs about the 35mph point, and transferred all the frozen solid meat immediately upon first loss of power... with a couple more frozen jugs (total of 4)....I did not open this chest until the afternoon of day 5 ...there was still partially frozen water, but the edges of the meat showed thawing signs... I cooked perishables first out of the "less efficient" cooler... a couple of gallons of cold tea, some lunch meat and hot dogs with IIRC 3 frozen gallon jugs... by the 6th day, we had resumed school, and I had access to one of the ice machines, and brought about 20# of ice daily to augment the coolers....after the first storm I purchased a 7 day cooler.... I had a generator for the 2005 season

for 2017 and Irma I forgot to get some bagged ice (mistake)but again loaded up the 7 day with frozen jugs, but by that time I had retired, was dining out for all meals, and did not store any frozen meat, only a few perishables... I had power by the night of the 3rd day, so only a couple of meals of hot dogs, a couple of egg and cheese sandwiches, and a can or two of chunky soup... I was supplying power to two neighbors so ran my refrigerator only for a couple of hours every six up until about 2300, and as a courtesy to the neighbors shut it off....two hours would put a skim of ice on the gallon jugs, and they really needed a little more time to completely freeze... a little planning and some bagged and solid ice worked for me, even without the high tech roto molded coolers

We own and use a 'briefcase cooker':

Briefcase Cooker

£9-£10 here and Butane refills £1 each. Very easy and very safe to use. Also an additional gas ring in the kitchen when needed, Christmas dinner, big BBQ, cooking at the table, picnics.

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A large (huge) vacuum flask may be used as a slow cooker, Pre-warm, fill with rapidly boiling stew, seal and only open when ready to serve.

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I have found it easy to get large 3-4kWh computer UPSs for nothing. Companies often replace the whole thing rather than just rebattery every couple of years and throw out the old one!!!. I have the heating boiler wired to a standard plug which is simply plugged into the UPS which is then plugged into the wall. It will run our system for some days easily, either bridging the blackout or giving time to set up an alternative

For camping - and power outages, we have the standard Coleman 2 burner propane stove, a portable / tabletop propane BBQ and also a MSR PocketRocket.

With plenty of propane and isopro fuel for these and along with a inverter generator to power the freezer and fridge, I think we are good for a few weeks of cooking. Any longer duration of an area wide power outage, then there may be bigger socioeconomic, logistical and security problems to deal with besides just worrying about cooking.

I have two Pocket Rockets, and they are the greatest - lightweight and hot! I actually prefer the original model, which I have used for about eighteen years, to the newer version. both get the tea brewing in splendid fashion...

I've got one of the old, standard, Coleman two burner propane stoves. Maybe a 1/2 dozen of those green propane cartridges, and then an adapter hose so I could hook up the two 20lb propane bottles from our propane grill (which we rarely use anymore, having gotten the Traeger pellet grill). I guess we could cook on the pellet grill too - we have many bags of pellets - if I hooked it up to the generator to run the pellet feed and fan. That seems like overkill, but it would work. I'll have to look how much power that draws, I may be able to power it off the small 400 watt inverter we have in the car and a disconnected car battery. I'm sure the grill will run on that, but maybe not the initial startup where it has to heat a wire to ignite the pellets. Maybe you could replace that automatic pellet ignition function with a few matches though. Or use the generator for power to initially ignite, then switch to inverter for run power.

I would be very doubtful indeed about the "briefcase cooker" linked to above.
Apparently they have a very poor safety record, with a number of explosions reported.
The failure mode is said to be leakage of the gas, which ignites and plays a flame over the gas cartridge which then explodes.
I prefer an LPG cooking ring with a large refillable cylinder that is a reasonable distance from the flame.

There are lots of different manufacturers of that butane stove design. We use one made by GasOne (same basic design but stainless steel body) for power outages here and no issues.

That said, it’s an open flame burner, so set it up and use it with that in mind. I recommend not using a pan that extends past the burner support. Using a large pot, pan or skillet that extends over the butane cartridge compartment is asking for an accident.