Okay, let's just assume that keeping tight temperature control is important and help the OP deal with his 110°F tap water...
Processing at 110°F/43°C is not really feasible for a number of reasons. So, whatever regime the OP comes up with, it is likely that a running-water wash will not be part of it (unless he buys an expensive in-line chiller). That means a fill-and-dump wash routine, which, although somewhat labor intensive, is a perfectly good way to wash. Wash time can be reduced by including a wash-aid step.
Assuming that the building/house/darkroom is air-conditioned, the easiest solution I can imagine is to simply keep all the chemicals and some jugs of water at room temperature and then process and wash at whatever temperature that is. As long as it's between 18° and 27°C, there should be no problems. The developing time would simply have to be adjusted for the processing temperature. Washing would be done with water from the room temperature jugs using Ilford's fill-and-dump guidelines (actually, I'd increase the wash time over what Ilford recommends). This would be easy, keep temps well within tolerance and only require filling up the requisite number of jugs with water and letting them sit long enough to come to room temperature. Even drying temps would be the same.
If the processing area is also quite hot, then using chilled water from a refrigerator or the like will be necessary. I'd mix all chemicals and the required amount of wash water to, say 20°C, just before processing and just let the temperature drift upward during processing. Assuming that all the solutions were in vessels of approximately the same size, the drift would be the same for all of them and, although the ending temperature would be higher than the starting, the change would be gradual and likely stay under 27°C by the end of the wash (if it doesn't, then a lower starting temp might be needed). Wash water would have to be in several containers the same size/configuration as the containers for the processing chemicals. I'd mix everything to starting temp then stick the thermometer in the last rinse-water/wetting agent vessel just to keep an eye on final temp. Development time would likely not need much adjusting from "standard" 20°C at all. An easy test of the viability of this method would be to fill a processing container with water at 20°C and then let it sit and note the time it takes to reach 27°C. If that time is equal to or greater than the total processing time, then you're good to go. Aqueous solutions take a surprisingly long time to heat.
Best,
Doremus