I doubt a heat gun could provide satisfactory results unless you are exceptionally skilled with it.
However, there is no reason you could not build an oven around the door. Is that easier than taking the door off? Probably not.
I am thinking taking one of these:
(175,000 BTU/hr liquid propane heater)
Bypass or modify the heater's thermostat to allow 350+ °F output, and build a heat resistant enclosure around the door.
This is definitely a DIY project if ever there was one with plenty of pitfalls and
excitement dangers. With adequate precautions, it can be successful:
- no volatile or flammable materials inside the enclosure
- the oven environment will be low oxygen and high CO2
- heater airflow will be challenging to manage
- temperature management will be challenging