I was just prescribed an epi pen for sudden allergic reactions. Is it safe to keep one in my car since they're sensitive to heat and cold?

No. My advice to patients regarding storing the epi pen is treat it like potato salad -- you wouldn't leave potato salad in your hot car all day and then eat it would you? Same with the epi pen. Additionally, the recommendation is that Epipen (epinephrine) always be on your person or immediately available for use. Severe allergic reactions can occur anytime and seconds matter.
Not safe in car. Epipen (epinephrine) is the most expensive medication you'll never use. I say that because its only used in the event of an unexpected severe allergic reaction and thankfully with awareness & avoidance that should be a rare event. Storing Epipen (epinephrine) in your car shortens its useful life. That increases cost & increases the chance that when you need it, it won't work because heat has degraded the medication.
Not in car. The epi pen should be stored at "room temperature" (around 77 f). Of course it isn't possible to always keep it at exactly that temperature. But if you keep it with you (briefcase or purse) and inside your coat in cold weather, it should prolong it's life. I recommend not storing the epi pen in your car.