My AE82 86kw Corolla does the same thing - more when the car's warm, the temperatures reasonably warm (not hot) and usually with the AC on.
Without AC it shudders and stalls when slowing down to lights after the car's been running for a while. It only does it when changing down to stop. If I just slow down in neutral its fine.
My diagnostic fault codes say there's a problem with my o2 sensor.
Other than that I have an unshielded pod filter which may be drawing hot air.
FWIW - I'm going to either shield the pod filter or go back to an airbox. If that doesn't work I'll look at the o2 sensor.
Maybe you should also check your diagnostics and see if it offers any clues?