iF PID is cycling like a switch, it's not configured correctly. Below is a link to my PID controller operator's manual. PID's have 3 modes of operation called: Proportional, Integral & Derivative. These are to be configured as a joint effort or a team of controls.
chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.auberins.com/images/Manual/SYL-2362%20instruction%201.6.pdf
I'll attempt to summarize: Proportional action: Sensitivity to deviation from setpoint; The further away (as in a cold pot/oven) the more power is delivered. Power is gradually reduced as "setpoint" is approached. If Proportional action or Gain is set to high, the setpoint will be missed, the power won't diminish in time, then will 'turn off' until the temperature is below setpoint, then power is applied too much & too fast, so it cycles off again to wait for the next cool down! Whew.
Integral action: This feature is used to essentially modify the Gain/Proportional setting by changing it based upon the difference between Setpoint & Process (pot/oven) temperature. That is, the closer Process & Setpoint approach each other, the smaller the Gain will be. (It's like walking slower as you approach the cliff?!?) There will technically be some Overshoot, but it gets smaller & smaller each temperature cycle. Now it's no longer a switch.
Differential action: This is more difficult to comprehend, as it modifies the effect of the previous two control actions.
E.G. From a cold start (pot or oven) the previous two control actions start reducing power soon after the Process begins to respond & starts warming. So maybe I'm the impatient type & want to keep full power going until the Process is only 10% away from the Setpoint, then backoff my contribution to the job & tell the P & I they can start taking over. That's the best I can tell that story right now. For perspective, Derivitive control action was designed to accommodate large or a slow thermal responding process, like a cold pot with 10# of lead! I sense you're thinking about your water heater; well that works more like a switch, as does your furnace & typical home HVAC. OH...Most of these PID controllers have "Auto Tune", so try that & interrogate the controller for the settings it derived for each PID function. I don't think those settings are saved, rather it starts over next time it turned on...
Techy's may criticize this explanation, so what, I tried. I can always discuss control theory & 40 years experience...that'll bore them to tears, eh Wally