Regulation of the temperature using PID
A PID only has one input and one output. In your case, the input will be the temperature. The use of the arduino would be to process the raw data of the temperature sensor and relay the temperature to the PID. Depending on the make and model of the PID, there could be certain transfer protocols you must adhere to. There are most likely open source libraries that will take care of transferring the data properly. 

Your PID is the piece of hardware that will "decide" when it is appropriate to turn the heater on and off, therefore it shall be responsible for driving the heater. That is what the output of the PID is responsible for. 

Lastly, your PID has a set point. In your case, the set point would be the desired max temperature of the plate. This set point is set and altered manually through user input. 

On a side note, if this is a personal project or a non deliverable, I'd recommend not using a PID. Try processing and analyzing all of the data exclusively on the Arduino, as it would be a challenging and rewarding task.