While a heat gun can remove a large amount of paint, there will always be some residue that needs to be removed with scrapers and sanding. Scraping can mar and gouge wood (less an issue when you can fill and paint) and sanding in tight crevasses in molding is hard.
There are commercial scrapers available, but they don't always fit your needs. On important projects, I have made scrapers out of large nails with their heads ground down to a sharp edge for tight curves and grooves, and pieces of curved cut glass for shallow curves (I'm a glass worker, so handling this risky stuff is comfortable to me, but not necessarily easy).
Sanding is tedious and, with old lead paint (yours looks old enough to be that), risky. You need masks and goggles.
You also may want to consider chemical strippers. There are newer citrus based versions that are a lot less caustic and foul smelling than the traditional solvent based ones. Even so, these will also need some scraping and sanding before finishing.
The wood had better be pretty good to warrant this care. If not either removal and replacement, or build up of new facing molding seems the better course.