What effect does temperature have on a mantis? (Please go in depth)
If a mantis were to molt, what effect does the temperature have on this?
-Ex: high humidity, but cold?
If keeping the temperature colder lowers metab and elongates life-why do many choose to head torwards the warmer part of the spectrum?
How important is it to vary temperature (at night/day switch)?
Basic pros/cons for too hot or too cold, please!
Unfortunately, your questions can't really be answered for "mantids", as there's too much diversity (~2200 species)! Which species do you want to focus on? You can read caresheets to see what others have observed about temperatures and each species (e.g. young nymphs stop eating when temps drop a certain level).
But I can say that most mantids do well with daytime temperatures around the 75-85F range while some from really hot climates would do best with 95F+. Some of the most popular mantids kept by hobbyists are tolerant with room temperatures but in general they like it warm and humid. Having said that, I think you're gonna see the most success with raising mantids (or anything, really) by duplicating their natural environment as best you can, including temperatures, humidity, day/night cycles, etc.
I'm probably just slow but when you ask "why do many choose to head torwards the warmer part of the spectrum?", what do you mean? Mantids thrive in warm temperatures but sometimes we keep males colder due to sexual dimorphism. If that's a new phrase for you, I recommend using the forum's search function for starters to read up on it.
I think it's important to vary temps, but I'd be very curious to hear opinions and findings on this. Mantids usually molt at night, so I believe allowing the temperatures to drop a bit during the evenings will help lower the likelihood of a mismolt (again, the nuances of ideal temp ranges depend on the species.)