Hello witness. I am a mountain search and rescue volunteer in south central New Mexico. Your question is one that I, too, have considered. First, I should like to say that I have no experience with either of the lights that you mention. But, I should like to share a few thoughts:
1. In my opinion, leaving anything for extended periods of time in very hot (or cold) weather surely cannot be good. I do keep some lights in our cars, but for extreme conditions, I move them in the house.
2. What I have been doing is having a BOB with various things, including light and batteries. That bag (in this case a Maxpedition Jumbo EDC Versipack) has a firearm, extra clip, knives, firestarter items, and various other personal survival kit type of things.
3. As for just what light is best for you, I have found that it really depends on just where and what types of SAR activities are likely for you. In my case, most of the searches will be in mountainous areas. A lot of the time, the areas are forested and a throw light may not necessarily be the ticket. As you know, SAR callouts usually are at night and lighting is very important.
4. Having said that, my strategy is to always have in my SAR pack or person: a) my EDC light (Fenix E01) plus extra battery; b) Fenix headband with CR123 form factor light (Lumapower Incendio; runs on CR123s, RCR123s). Then, mission dependent, I have two lights that I take with me to the base command and decide which of them is best. One is an Olight M31 (2x 18650s 3xCR123s, or 4xCR123s) where throw is needed. I got this light about 2 years ago and it, at the time, was one of the better throwers on the market. I am happy with it. Now there are numerous other choices out there that are better. But, my light is paid for and fills the bill. I just recently got another light that is more general purpose. I chose a Sunwayman V20C, which runs off of one 18650 or 2 CR123s. It goes up to about 445 lumens otf, and throws ok at 100 yards. I like the variable control ring on it; moreover, it's form factor is in between the Olight M31 and the small Lumapower Incendio for dimensions and weight. Bottom line: I will carry 3 lights with me on a search.
I hope my thoughts are helpful to you,
Regards,
Steve