Imagine you're watering the lawn and someone lifts up the hose and plonks some of it it in a lit fire. You will notice the temp coming out of the hose has increased.
- If you slow down the flow rate the temp will increase.
- If you coiled the hose into the fire a few times the temp will increase
- If you increase the heat of the fire the temp will increase
- If you light a second successive fire and lay some hose in that, the temp will increase as would another and another. (this would also give you more tune-ability as you could take the hose off one of your ten fires and slightly reduce temp etc)
Once you were happy with the temp you pull some hose back out, stop stoking the fire, put one fire out etc. This is where you would start tuning your temp and your Heat Exchange.
Imagine putting a pot full of water on the fire/s instead and you put the hose in that. All of the above would still apply but now you would have a more stable heat exchange. It is more stable because the flames aren't just hitting the hose here and there, they are heating the bottom of the pot which is heating the mass of water inside. Oil would be more stable and is used inside the jacket of some mash-tuns. So you could imagine your pot being full of oil as well.
Now imagine that the water is not coming from the tap but from a tank instead. The hose comes down from the tank outlet and feeds into a pump. The pump pushes the water through the coils of hose inside the pot/s and back to the tank. The tank water will slowly warm up. To measure the maximum temp that the tank water is getting heated to, you might have a temperature gauge on the outlet of your hose as it exits your pot (which you could now proudly refer to as your HEX ~ Heat Exchanger).
Instead of having a fire you now have an urn (or a few urns) and you put your coil of hose in that instead. You understand that you can change the temperature of your urn and you can set it to maintain your desired temp. There may be some fluctuation in temp as it possibly drops a little just as the temp has dropped and it registers that it needs to turn on.. It will also shut itself off the boil once the target temp has been achieved but may end up slightly over-shooting the temp. After a while you would learn to predict those overshoots and tweak your Urns temp to get a closer, more stable set-temp. That is what (amongst other things) a PID would do for you. It starts to tune the temp to lessen the temp fluctuation. I do it with the round knob on an Urn with my hands. In music terms you could ask yourself if your a DJ that uses a computer to mix your music or knobs and buttons where everything is more hands on.
As you now want to take the temperature higher and then hold it, you would turn the knob on the urn up to your set temp and you may also slow your flow rate by partly closing the valve. A PID would start backing off the heat as it neared your desired temp. A PID may have had all the times and set-temps set in it's memory and you walk out to a mashed-out beer ready to transfer to kettle.
Hope that helps. Excuse the spelling, grammar etc - no coffee yet and it's calling baby