Will sheet aluminum - as in an aluminum cup - withstand the heat of wood fire coals? I chose stainless steel because I thought it is more melt resistant than aluminum.

I just chose SS because it was cheap and available and fit my bottle. Had Ti been at the same store I would have been just as likely to chose it even though it would have been more expensive.

Sheet aluminum will not stand up to any flame source as well as steel or Ti, it will work for a limited period of time. I would think for a survival situation it would last plenty long enough.
I've used the same throw away pie tin for melting wax over a low flame for a couple years now, and it seems to be doing just fine. It is getting a little beat up, but it still does the job.

Given time, even cast iron will not hold up to repeated firings. I can already see wear on my oldest skillets which are used often enough in open campfires. Ti will likewise ablate, as do any metals subjected to oxidizing action, just at different rates.

In fact, there are dutch ovens made of aluminum, some have been used over open fires for years. They do wear, but they remain just about as usable as anything else.

For survival, though, I don't reckon there's that much advantage of aluminum over steel insofar as weight is concerned. The only other concern then would be price, which can be significantly different.

The weight savings of aluminum vs stainless are large. Did you mean Al vs Ti? Question is why pay for titanium instead of aluminum?

I guess a titanium mug is better to hold in your hand and drink from because of Ti's lower heat conduction. I like titanium (or ceramic or Lexan) spoons for the same reason.

Isn't TI more conductive?

Go with the single wall,you can heat stuff up with it . the dbl. will deform with direct heat . If you want to keep the content's warm slide and old sock on it. the sock come's in handy as pot holder/wipe down / bottle insulater

No, Al is much more conductive than Ti.

Hate it when I'm wrong.

S/S Oli cup $5.99 at Campmor.
I don't mind cooking on a fire with this one.
You can carry 2 on a Nalgene bottle. Top and Bottom.

Yes, aluminum vs stainless, and you are right, but at the scale we're talking about, I think the relative weight for one cup in the pack will feel indistinguishable based on what it is made from, maybe even two.