I have found that with my heat triggered migraines that coming directly out of heat into AC tends to make them go full blown fast.
If I have been in the heat and feel the twinge of the migraine beginning and can do a gradual cool down the migraine doesn’t seem to be as bad. If I am outside and one begins, I try to locate a place a few degrees cooler and stay put for a little while before moving into the AC. I think that by going from heat to cool that it is a shock to the system and that is what helps to make the migraine go full blown in a matter of minutes.