I only ask because I'm making up a controller for one. I don't find
the 3 heat settings provide enough choice so I'll be controlling a
small triac via a PWM chip. Although the max current draw of this
appliance is only 350mA, the triac (a Z0607) is pretty puny and I
don't want it operating at too close to its max ratings obviously. I'm
using a snubber to be on the safe side WRT to back EMF anyway.

Here's the datasheet for the triac:

https://www.st.com/resource/en/datasheet/z00607.pdf

Will that do it or is something more meaty required?