Gaalfred, If you want cheap, get rid of the VFD. Open mind. I'll talk you through it. OK we change rediculous to unfortunate??
Pump head output (affinity law) varies with the square of pump speed. That's only 1/2 of the problem. The other half of the problem is the system curve; ie what's going on with flow and head in the pipe and tanks. The system flows vary more or less with the square root of pump head. Additionally they can have an initial H0 representing static head of the discharge tank that the pump must begin to pump against when starting. NPSH can also adversely affect this. So head obviously changes as the pumping continues and the discharge tank fills. How that changes is affected more by the dimensions of your tanks; ie how much head has increased in the discharge tank, and maybe the supply tank too, for any given quantity of fluid pumped. That is related more directly to tank fluid elevations than it is to flow rate. As you can see the resulting complex relationship is nowhere near direct to pump speed. If you could make a good mathematical relationship to describe it, it would not match how your PID would take temperature input and then output an instantaneous pump speed.
You've got two problems going on. Flow control and heat control. You apparently need flow control, I imagine to be as constant as possible, so you can know tank fill and process stop times and all those scheduling things that are good to know, and so that your heat exchanger can operate at a nearly constant power output. Wild variations in exchanger output power output doesn't do anything any good. Radical flow changes would cause wild temperature and power fluxes at the exchanger even if the milk remained the same temperature during the process.
When faced with multiple tasks, I like to break them down. Flow control is one, temperature control the other. Pump control works well for flow control. Exchanger power control works well for temperature. Those two working independently takes away the ability of each to fight the other, which would happen if you tried to control flow and temperature with only one feedback loop. So, use some kind of flow control for the pump and a temperature control to adjust the exchanger power input for discharge temperature.
Once you separate the two control loops, the pump is free to operate at constant speed for the process, if the flowrate is right at that constant speed, however you also have a wash cycle, WHICH IS COMPLETELY ANOTHER FUNCTION. So you need another button to turn these loops off and switch to the wash cycle. But forget that for now. If the flowrate of the pump is not right at it's syncronous speed, you could change the speed with a VFD, or you might could run at synced speed and use a control valve to control flow. Control valves can be far easier AND CHEAPER means of flow control than buying and installing VFDs due to cost of the VFD over the small control valve the previous mismatches I mentioned in pump head output vs flow in the system with tanks. Control valves don't suffer those head vs flow problems as much as pumps can. So I think that with proper tank dimensions, you could run the pump at sync speed with a contrl valve for flow and use a temperature sensor feedback to control the exchanger's function directly with the output temperature.
Technology is stealing American jobs. Stop H1-Bs for robots.