After doing some tests with the PID library I realised that this type of control might be overkill, and a simple comparator that enables the output when the temp is lower than the set point is enough. Still I haven't done the complete test yet as the precise temperature converter is giving me an error. So this is yet to be concluded.

But this raised the idea that I can completely overhaul the whole design and create an alternative that can be super simple.

I could use a analog precision op-amp to amplify the voltage of the thermocouple and output a voltage that represents the temp mapped as voltage: 10mV equivalent to 1 degree Celsius. Then a maximum of 450 degrees would output a 4.50V for example.

This output will be compared to a voltage referenced to ground provided by a regulator. A simple trimpot will set the target voltage-temperature.

So a second op-amp will act as a comparator and will do this operation, switching on the driving transistors when the temp is lower than the setpoint, then switching them off and perform the measurement to see if it's the case to switch them on and off again.

A RC oscillator to create the loop and some low pass filtering will provide the stability of the system.

The circuit will be entirely analog and the display part is made by measuring the voltage with a voltmeter, the simplest form of the controller involving only a couple of op-amps, resulting in a very simple and small board. Not the most useful but still very portable.

Next I will continue to develop both circuits and compare the final versions.

*both can be powered with a battery pack at 12V or trough a DC-DC converter at 24V 70W for full power.