First of all, I’d recommend some sort headlamp to free up the use of your hands. In my case, I’ve got a baseball cap with a AAA flashlight reverse clipped onto the bill. I find the cap helps fend off the weather a little and the small AAA provides more than enough light for things like fixing a flat tire.
I’d suggest carrying a flashlight with diffuser to use as a backup flashlight and as a traffic baton. Also, pick up some glo-sticks or flares for emergency markers. However, personally, I am guilty of procrastination and have not gotten around to picking these items up. 
As far as batteries are concerned, if the temperature drops below 20F degrees, then your only good choice are lithium primary batteries. Otherwise, above 20F, li-ion rechargeables are okay. Above freezing, NiMH batteries work well. And alkalines are best used above 40F. So, for most folks, the choice would be between lithium primary batteries and li-ion rechargeables.
- If you just want an emergency flashlight to store away and forget about it until needed, then lithium primaries are your best option.
- If you regularly use the flashlight as the “car flashlight”, then you’re really not going to be able to reliably tell what the charge state of the battery is unless you regularly maintain it (replace or recharge). In that case, li-ion rechargeables might be the better option.
Regarding the concern about batteries baking in the car under the hot summer sun, opinions are mixed [link].
Your decision on which flashlight to store in your vehicle will depend on your climate, your choice of batteries, and your budget.