Control this induction heater circuit with Arduino by breaking into feedback.

here is a circuit.
Can I break into this circuit around where resistors R1, R2 are connected to 15 volts power supply and add a component that would turn enable or disable the circuit?

I would like to control this circuit with an Arduino, switch it on when temperature goes down, switch it off when temperature is above a specific sensor input value. (Like a thermostat)

Something tells me that there is a smarter way to control this circuit that by cutting power to it.

What would be the current that is going through R1+R2? Is it a good place to install a transistor?
How would the new circuit look like?

Thank you!

You could put a N-channel MOSFET between T1 and T2 Sources and Gnd, when open there is no Gnd thus no current flow, when closed circuit works normally.
AOD514 from Digikey would work well, Arduino can drive the Gate no problem.

High-side switching of the 15V to the gate resistors ought to be enough, if a pull-down resistor (much larger in
value than R1 and R2) is added too.

To high side switch you need to level shift first with an NPN transistor, say, and use PNP or p-channel switch.

Bit uncertain whether the transients on switching off are going to be safe though - potentially large
currents might flow through both devices together at that point.

Any way I can directly use microcontroller's PWM to drive some semiconductors that would in turn oscillate an induction heater coil? I have looked at carious circuits that use PWM for induction heating.
There is a number of them that uses 555 timer.

I would like to know if anyone had anything like this built and tested.

555 can work on a wider voltage range than Arduino. So some isolation and voltage level accomodations may need to be made.

I am not making a very powerful heater, only to heat 2 grams of steel.
Yet I would like to keep things simple and compact.

The circuit shown is resonant, and finds its own frequency which will vary with the loading.

Using a fixed frequency will not be as efficient unless you track the resonance somehow.

The self-oscillating LC tank circuit above is about the simplest induction heater circuit
you can imagine, which is why its commonly used for induction heating, camera flash
inverters and so forth