Have you tested for lead paint yet? Kits are available at home centers, paint stores, etc.
Follow the instructions carefully, including the instructions that explain how to test the kit itself. A negative result of a paint test isn't a valid result unless you know for sure that the tester itself is working. The kit provides a method for checking the kit itself.
Using a heat gun will results in fumes, probably more (and worse) fumes than stripping. Even outdoors, a fan to quickly move the fumes away couldn't hurt.
A heat gun can also damage (scorch) the wood. Since you are painting, that may not be an issue, but if staining is in the door's future, just keep that in mind.