Sounds like the issue is once the car is warm. This can be heat affecting the coil or leads, or carb is running rich, which when cold is ok but once warm could be too rich for idle and cause stall.
Check the resistance in coil, hot and cold, and test resistance in leads. If they are ok then I would check and clean out the carb you might have got dirt in one of the passages when you kitted it.
If your choke is auto check its not getting stuck.
If you have accuspark ignition I doubt it has anything to do with it. Its just electronic points so if there was a problem with it it would show up at all revs and temps, not just hot idle.
That said, if its just at idle and drives well in mid range, no misfiring, then my money would be on the idle circuit or choke, and it could be as simple as you didn't adjust the idle screws properly when you kitted it.