Regarding drive for heaters
A VFD is not the right device, and might well have problems because the drive would not be able to detect the expected back EMF for sensorless operation.

There are two typical  strategies used- time proportioning where the heater is turned and off for varying duty cycles. The period might be a few seconds if solid-state switching is used, up to perhaps 20-30 seconds or longer if a mechanical contactor is used. 

The second method is to use a phase-control method to provide smoothly varying power, which of course requires semiconductor switching. This is less desirable because of the heat and electrical noise caused by the (usually) thyristors. It's also a bit less desirable from a control point of view because of nonlinearity. If your heating is primarily IR such as halogen tube heaters you may need to use this method because the variations would otherwise be too large.  

The most straightforward method is to buy a self-tuning PID temperature controller and sensor, and marry that to a suitable power switch, and most industrial applications use exactly that approach.