High power power regulators - thyristor regulator?
350kW? so you will have 3phase input

One option you could use is in-line thyristors







simulate this circuit &ndash; Schematic created using CircuitLab

How to control?
You could do a simple BANG-BANG &amp; fire all 6 SCR when the temperature falls too low &amp; turn them all off when it gets too high.







simulate this circuit

This might be adequate BUT with a high pulse in output power. A bit more work and you can do phase-control on the firing of the SCR. This will reduce the power driven to the heater to then provide a smoother temperature control

One thing worth noting!  you are dealing with 350kW &amp; there is going to be a large power quality consideration to worry about ( you will be charged in VA &amp; have a tight power quality profile to match).

While phase control will give you a nicer temperature response it does mean you will need to think about the AC side draw a bit.