Before I do anything, I am going to do as you suggest. It is starting to cool off a little bit. I'll see how it does when the temps are cooler. I never have a problem restarting. It always starts up immediately first crank. It is on initial acceleration in first gear when it sputters. Again, thanks for the input.
I am still leaning towards "heat soak" and the crappy gas we have today, so I would see if cooler outside temps cure the problem. But, it could still be something else if you want to explore further.
It could also be the accelerator pump in the carb worn out or going bad. It is not giving th carb a good "squirt" of gas when you first open up the carb on acceleration.
The carb opens up and engine vacuum drops creating a lean condition and the extra shot of gas from the accelerator pump feeds the engine through this momentary low vacuum condition to richen up the air/fuel mixture so the engine does not stumble and picks up as intake velocity increases to pull fuel through the carbs venturies.
However, if this were the problem, you would experience this under all hard acceleration conditions, not just first gear.
It could be an electrical problem as My65Goat has suggested - weak coil, point gap needs to be verified, points may need replacing, or might need a tune-up if this has not been done in a while.
Your vacuum advance/timing could also be suspect. If the vacuum advance is not operating correctly this could be giving you a problem. When the car is running, it is at its highest vacuum point and vacuum advance at full operation. Once you accelerate hard, vacuum advance is eliminated and the engine operates on mechanical advance - initial advance at the crank and mechanical advance through the weights in the distributor. If this is not adjusted correctly, to include your advance curve in the distributor, it could cause the same effect as you are experiencing on 1st gear acceleration only. Once rolling and the engine in higher RPM's in other gears, you may not experience this hesitation due to the higher range of the RPM's. So it is important to know intial timing at the balancer, how much/maximum mechanical advance the distributor provides and at what RPM that is, how much vacuum advance your vacuum can provides, what your total mechanical advance (initial + distributor) and at what RPM this is reached, and then what your total mechanical plus vacuum advance is. All these specifications will dial-in your timing and the advance curve of the engine. So, that stumble could be caused by a timing issue.
I might simply advance the distributor a few degrees to see if the stumble improves or goes away. CAUTION! If in advancing the timing for this test you hear any kind of engine "pinging" or "rattling" from detonation, take your foot off the gas pedal - your timing is too far advanced and you do not want to damage the engine. If it does improve your problem, return the distributor back to its original setting so as not to have timing too far advanced and then go about tailoring your engine timing to bring it to where the engine likes it, not what the owners manuals say to do. Just a couple of advance degrees at the crank pulley can make a big difference in engine performance.
So a few things to look into and check. To know what it is, sometimes you have to check/adjust things to know what it isn't.