Thanks, how about dimming the output of the IR lamp?
Also, for inrush when turned on at low temperatures, we need an NTC
How many 'engineers' does it take to
replace turn on a light bulb?
So here's a few relevant observations about turning on an incandescent light bulb.
First, if you limit the current to the amount that the bulb will draw when warmed up--in your case about 2 amps--the bulb will turn on a bit slower but typically not enough to matter. You might not even notice in the case of smaller bulbs. So if you had a huge bulb or bulbs in parallel that drew current that was a large fraction of your circuit breaker or fuse ampacity, inrush limiting might not be totally insane, although I personally haven't seen it done on anything short of large commercial devices like theatre lighting where they soft-start via dimmers. A single IR-heater that draws 2A on a 16A circuit really shouldn't need anything at all. I have 500W (250W x 2) IR heaters in my bathrooms that run off of a 15A 120V circuit (not dedicated) so they draw ~4.5A when on.
Second, if your bulb does fail at turn-on and even if it goes short, those faults clear very quickly--at least the ones I've seen. Also, I think the IR bulbs like the one you mention aren't all that likely to fail short and they typically have pretty long lifetimes. If you still want to incorporate short protection without blowing your fuse (and you absolutely need a fuse...) you'll need to passively limit the current to something below what would blow your fuse in less then 1 cycle and then have an overcurrent detection system that will shut the power off at the end of the current half-cycle. That's assuming you are using a triac.
Third, bulbs like that have fairly long thermal time constants. Both soft-starting and dimming could be accomplished by cycle-skipping rather than phase control. Perhaps a 5-cycle (100ms) period with dimming levels from 1 to 5.