You may or may not need a new carb, possibly rebuild your existing. You know heat is the issue so this leads me to believe that expansion or evaporation is the issue. If you think it's lack of fuel due to evaporation (or starvation) here's a little trick to verify. Buy a cheap can of starting fuel, duplicate your exact situation, then spray a bit down the carb. If it starts immediately and stalls, fuel never made it to the cylinders thus the carb is low in the fuel bowls or your vacuum is low or your fuel pump is at fault. Possibly a worn fuel pump rod. Timing could be at issue for low vacuum and if the carb bowls are empty, the carb has leaked down causing a rich state in the cylinders which is why you have to push the pedal when hot. In essence, when you push the pedal down you are allowing more air into the cylinders to put the air/fuel ratio in a more combustible ratio and bypassing the idle circuits in the carb. You should check the throttle blade's opening when static according to OEM specs (or whoever's carb you use ), block all vacuum feeds to the carb temporarily (power brake booster, PCV) to eliminate initial vacuum loss and retry the same way.There are other reasons for low vacuum including worn piston rings (low compression) poorly seated valves, worn valve train components and carbon build up. Know your vacuum at idle and with a proper vacuum gauge and it's use much can be revealed about the engine, timing etc. As far as the carb is concerned it would be great to have a loaner or spare for elimination purposes. Do a fuel pump volume test according to the service manual with the coil primary removed - a friend or remote start switch will be required to do this. Your results in these tests will surely point you in the right direction to remedy the situation.
