A VFD in scalar mode (V/Hz only, no vector control) will work, but not well. The VFD changes the voltage and frequency to a MOTOR using DC pulses because it is feeding an INDUCTION circuit, and it is the inductive time constant of that circuit that allows the PWM to approximate a sine wave. If you have a resistive heater, there is virtually no inductive circuit. Frequency control means nothing to a resistive heater, what you want is voltage control and without the induction in the circuit, you don't have much control of it with a VFD. I have used resistive heaters to test the VFD as a general load just to make sure the VFD worked, but the control of that heating load was irrelevant for that. As an experiment once (after a similar discussion in this forum over a decade ago), I tried it again and it was extremely inaccurate. I could make a big change in my output command and it had little effect on changing the heating effect. But by increasing the carrier frequency to 16kHz as suggested (by I think Gunnar), that did improve the control performance of the heating effect somewhat, probably because the higher switching rate made the entire circuit look more inductive. But that requires de-rating the VFD current capacity by about 50% because of the added switching losses in the transistors. All in all, it's a waste of money, because a simple SCR controller does the trick for 1/5th the cost, maybe less once you de-rate the drive.
That said, if it is an INDUCTION heater, that's a different story, PWM is used for that all the time. I have also wondered if you used a transformer between the drive and resistive heater, if that would give you more control. Probably would (because of the inductance of the transformer) but there are potential issues with using transformers with variable frequency, so you would have to try to modify the VFD output to change voltage only, and few VFDs are going to allow that. It's not what VFDs are designed to do...
"You measure the size of the accomplishment by the obstacles you had to overcome to reach your goals" -- Booker T. Washington