During winter use is it less expensive to: set the thermostat to maintain a set temperature or have it come up to temperature during its cycles. My wife & son argue that its more economical to maintain temp., I said to bring it up on each cycle: Who's going to eat crow?

My guess would be that the best answer is: it depends on how fast your tub loses heat and what your timer settings are.

If it loses heat slowly, using the thermostat might cause it to kick on a couple times a day. If your timer settings make it come on more than just the thermostat would then the thermostat is the way to go. This wouldn't account for any filter cycles where just your pump was running but I doubt you'll notice that on your bill.

If it looses heat quickly and the thermostat makes it come on for a total time longer than the timer would, then obviously the timer would be the way to go. However, with the timer there's no guarantee your tub will stay up to temp and you may need to heat it manually before getting in. Obviously that would make running it on the timer more expensive but no one can tell you by what factor.