heat is a definite enemy. Dirty contacts is a close second. I've been in your shoes more times than I want to remember- sitting in some parking lot waiting for the thing to cool off.
Pontiac had a special part number for a HD solenoid for Firebirds, and there is also a factory heatshield. I think the HD setup was on all V8 Firebirds, but maybe it was just the 400s.
If you or someone else replaced the solenoid from a generic parts store, it will be the generic Pontiac solenoid, not the Firebird. And, most likely your heatshield got lost over the years.
After going through about 8 starters/solenoids over the years, I finally figured it out and got the correct factory starter and solenoid, and added an aftermarket "space shuttle tile" heatshield. Also getting rid of my headers helped!
I think Year One should have the solenoid and heat shields.
John
ps- also make sure your timing is not too advanced!