Any type of heating or cooling system that uses outside air should be turned off and the vents or openings to the outside air blocked. (except in the extremely unlikely case of the system being designed for use under fallout conditions.)

Any type of flame based cooking or heating should be avoided.
Stock warm clothing, many changes of long underwear and plenty of blankets, preferably wool blankets.
Keep supplies of food that need no cooking and can be eaten straight from the packaging. Lifeboat rations, dried fruit, chocolate bars and the like.
In theory electric heating or cooking could be used, but it is most unlikely that you will have utility service. Do not rely on a generator.
Remember also that water will almost certainly be much too valuable to use for anything but drinking.
No laundry and no dishwashing under shelter conditions.
"water means life, do not waste it"

In warm climates, stock plenty of changes of lightweight cotton clothing, wear as little as decency permits. Consider sacrificing decency to survival.
Battery operated fans help comfort despite not actually reducing the temperature.
In very hot climates where survival without cooling is doubtful, more extreme preps are called for including bulk ice storage.

Provided that you have a serviceable Geiger counter, preferably two counters, you may judge that the radiation level has declined enough that BRIEF visits to the outside are now an acceptable risk, but that remaining in your shelter for most of the time is still prudent.