I've just joined up and came across this thread. By coincidence it was I who invented the Pre-Soak Temperature Calculator for the Paterson Orbital Processor in the 1970s when I worked for Paterson.
The temperature control system is pretty much as you have all described it except that it relies on a pre-soak of a large volume of warm water to bring the temperature of the processor somewhat above the temperature you want the solutions to be at. As you surmised, the temperature will fall gradually back down through the room temperature to provide a satisfactory average over the development time for a print. The subsequent solutions are not very critical as long as you give enough time. You can't easily overdo them! The Processor and the solutions should all be at room temperature. A minor issue is that you may need to raise the room temperature a bit if your solutions have to be very high, after all you can't very well pour boiling water onto your film or paper!
I still have a Processor and have recently decided to revert to large-format photography just for fun and intend to process 6.5 x 8.5 inch film in it. I know the requirements for paper and film are a little different but I know a couple of photographers nearby who do that already.
I have a copy of the original instructions but not the pale blue and white Calculator. Would anyone care to swap a scan of the Calculator parts for a scan of the instructions? I could repeat some of my original tests but it would save me a bit of bother!
In any event, if I can answer any other queries on it I'm always glad to help.
Regards, Pixal8