Correct, Heat tempers parts, but not all tempers are the same.
In general, higher temperatures and longer times result in softer, weaker parts in the same alloy.
The tough question is were critical parts that will be exposed to 375 F in this process intended to be tempered at a higher temperature or for a shorter time at 375 F.
The 375 F range is approprate for tempering some steels to specific hardness and strength ranges. This would typicaly be hard, high strength applications.
So, is 375 F for 3 hours safe. Dont know without knowing the alloys in the gun and what the current hardness and strengths are.
Could be the parts were drawn at 900F for an hour and exposure to 375F wont be a problem. Could be they were drawn at a much lower temperature.
Most of the tempering charts I have seen have values below 200F on them. This is typicaly for very hard parts (punch dies, end mills, etc).
I also recall that the charts had a standard drawing times of about an hour.
(any stainless, aluminum or other alloys that are not hardened by martensitic transformations and the problem becomes even more complicated)
Yes, there is a lot of old info out there about home shop tempering. The rules of thumb are ok for parts that dont fail in manners that harm the operators.
A lot is based on stuff written by blacksmiths useing simple carbon iron steels.
Chrome, Ni, Mo, and other elements all change how easily an alloy tempers. These elements are all common in steels used in firearms manufacturer.
Going by color or flashing in a pool of oil to judge the temper may be fine for hammer springs, but not for locking lugs on a breach.
No good way to know without being a lot more farmilear with the gun.