I know what you are saying and I do the same on the highway n hot summer temperatures. It may be hot but still runs well. This is a case in 60 degree weather misfiring over 2000 rpm after idling for long periods.
I think its fuel percolation - But not so much the engine temp, rather the fuel temp is the problem. I have been fighting the same problem and I believe it's down to air flow - when you are on the highway there is lots of cooling air flowing past the carburetors and fuel lines but when you are sitting idling there is little air flowing past the carbs and fuel lines. Heat soak from the head and manifolds slowly heats the fuel and it vaporizes.
This is the same phenomenon we know as "hot restart" problems when the car runs like crap for a few miles after a short stop to get gas or take a break. After a couple of miles fresh, cool fuel to the carbs settles things down and it runs fine again.
I have 2 5wire UEGO air/fuel monitors in my car (one in each header collector) and when the stumbling happens I can clearly see the A/F needles swing rapidly all over the place from rich to lean corresponding to the sputtering of the car. I think this fluctuation reflects the liquid vs vapor in the system - carbureted engine MUST have liquid fuel to meter correctly. This is why, in my case anyway, I'm confident it's not some electrical issue.
I've been researching the issue a lot lately and several things I have learned - One reason we are suffering this more these days than the past is the formulation of gas these days is a lot different than it was in the 50s, 60, and 70s. Some of the additives have a lot lower boiling point and vaporize easier, most modern fuels burn much slower therefore getting the exhaust hotter than it used to be (some are finding advancing the spark at lower rpms helps because the slower burn rate needs more time to fully combust inside the combustion chamber rather than still burning in the exhaust tract). On top of that, there are very few carbureted engines so they formulate for fuel injection which is at much higher pressures and may not be as subject to fuel vaporization as our 2-3psi systems.
I think one of the main problems is the fact that our fuel systems are dead heading - when the float chambers are full, the flow cuts off and the fuel then sits in the lines and has time to get hot. One of the solutions is to have a bypass system with a return line to the tank so when the float chambers get full, the fuel continues to flow so it doesn't sit and get hot...thereby getting a continuous supply of cool fuel from the tank. Datsun did this with the 240Z when they copied the Healey and most all modern fuel injected cars do this.
One solution I'm playing with right now is blowing a cool air stream onto the carb bodies and float chambers to help keep them cool. I have made a 'manifold' out of pvc pipe that is mounted just below the carbs with holes blowing air up to the base of the carbs and float chambers. I have a thermostat snap switch set to on/off at 140F as an initial test (I have read that a lot of modern fuels evaporate around 120-140F). I found a small 12v computer cooling fan I mounted in the bottom inside of the inner fender well for a source of cool air. I'Il have a chance to drive it in a couple of days and know more then.....
If I don't get some success with that approach, I plan on getting a bypass pressure regulator and plumbing a return line - but since that is a much bigger project, I decide to try the 'blowing cool air test' first.
Not a very good picture but shows the general idea (and obviously temporary with cable tie mounting) - if it works, I'll make something much nicer