Well lets get the system together and see what you think. A scope would do it.
Most of the time if you have temperature problems with a 555 circuit it is because of the capacitor used in the timing circuit. It's easy for them to vary a few percent over temperature, but if you use a cog or npo they are quite stable. See this write up in the spec sheet.
https://www.mouser.com/Search/Refine.aspx?Keyword=c410c102j1g5ca
Attached is a timer circuit that should work. I'll add the circuit to keep both fets from being on at the same time later.
Do you have what you need for the power supply?