This issue is not only applicable to ammunition. Withing a well equipped kit there are a lot of things that could be potentially damaged by the heat. Food and medicine degrade with heat.

The heat in a car, short of the vehicle actually being on fire or the ammunition being placed directly over a defective catalytic converter installation, wouldn't likely cause the ammunition to cook off and short of that it should remain usable for a long time. That said the heat certainly isn't doing the cartridges any good. For a critical one-time-only shot and a choice between ammunition stored in a controlled atmosphere or ammunition stored in a car trunk for a year I wouldn't be reaching for the stuff that had been riding in the car. Common sense.

I have found that if you are going to store things in a vehicle you can limit the heat exposure by storing materials as low as possible and using insulation to moderate the temperature fluctuations. An inexpensive Styrofoam cooler kept low is good. There is a common building insulation available in many hardware stores based on foil and bubble-wrap. This can be used to make pouches, envelopes and bags and it can be doubled or tripled to get significant amounts of insulation in small areas and with little weight.

http://www.reflectixinc.com/images/uploads/allpdfs/f8%20retail%20product%20guide%200107.pdf

You can also include bottles of water in these packages to further moderate the temperature extremes. Just make sure they are sealed and kept upright if possible. This lets them do double duty. Your going to need the water anyway. If the other supplies are very sensitive to water you might leave out the water or, perhaps, substitute gel packs.

When storing supplies on a vehicles floorboard be aware of the location and routing of the exhaust system and catalytic converter. These components get hot when the engine is running and stay hot for a time afterward.

Also, particularly if you traverse deep water, drive a junker, or simply have leaks, portions of the floor of a vehicle may get and stay wet. It wouldn't do any good to prevent damage from heat only to see your supplies damaged by water. A cooler or ammo can may be a good way to keep any water out.