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Temperature control. A decent heat gun will let you regulate its output to a level that won't cause celluloid to burst into flame, which it has a tendency to do at around 165 degrees.

Where's the calibration on an open flame, and what kind of open flame were you suggesting? Different fuels burn at different temperatures.

An alcohol lamp, which burns at a comparatively low temperature, was the traditional heat source for pen repair for many years, but it took a bit of experience to know where to hold the pen to get it hot enough for the shellac to soften (145 degrees, if I remember correctly) without melting or burning the surrounding pen material. You only have about twenty degrees of wiggle room there with celluloid pens.

Ideally, you want a heat gun with a variable thermostat. Even a blow dryer can be too hot for celluloid.