The drive for me is absurd.
The heat is a big, who cares, I'm not sure if anyone reading this even bothered to ask if this is a midwestern gig?
It can be warm, but on average it's not that bad. Rarely something to cancel any type of outdoor activity over. And if it does turn out to be the case, just take more breaks.
To me the most important question is what kind of music are you playing. Can you just sit there in a chair playing entire songs with just with one finger. Or are you out there trying to pull off Led Zeppelin tunes?
The big thing for me is if the promoter is out to lunch, show up but throw 165 songs out the window.
Also work out a set list where you can rotate players, and again that's if you're just playing very simple 1 finger bass lines.
That being said, it sounds like your bandleader/whatever has no idea how to negotiate. Whoever did the hire, had no idea what reasonable terms even sounds like. That's a situation that is open to renegotiation, I'd do the gig, but only for the bragging rights.