Paint bubbling and peeling on a steel door
I'd bet on "poor preparation/paint job" (given that preparation is 90% of a good paint job.)

If you wanted to, you could use a high-temperature paint such as engine enamel (typically good to 450F or more) (no need to go for the exhaust-manifold paints unless your doorframe is charring, I think.) I strongly suspect that's not really needed; you could put a magnet on a thermometer and stick it to the door to get a reading for what the temperature actually is some sunny day.