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Morning and welcome to the forum!! I’m not real familiar with the term “time proportioning control”, however, I’ve done quite a few temp controls. Also Fred, the forum guru, has a lot of videos on PID control.
Anyway, you have a feedback for temp from your process. I would use an “on-off” type of control and not so much a PID loop. Since you have a solid state relay, that is either on or off, doesn’t modulate, so to speak, like a gas valve or a steam valve for heating and burner control. I would have the code control the relay with a limit instruction or maybe compare instructions, and with a little tweaking you could program in logic to anticipate overshoot and basically have a stable process. Hope this helps, and again, welcome!