I’m going to 2nd, 3rd, and 4th BeeHoney.
All I ride are OTTBs. Feed almost NEVER affects hotness. That is an old wives tale well debunked by equine nutritional studies.
My last upper level horse was perpetually a kite. Seattle Slew grandson. Could jump a car (literally did when they were used on xc as fences). The best way to settle him was 5 minute 3/4 speed gallop sets on a 1/2 mile butte that took us 30 minutes to ride to and from. I would do that at least twice a month in the off season.
Good OTTBs are bred to have no bottom. They will kill themselves to run. That is what their heart and DNA tell them to do.
I would get out of the arena. Trail ride, gallop, even do dressage and other flat work anywhere else other than the ring. Galloping and jumping in the snow is a blast! Gotta be safe about it though. Trails help the horses focus without pressure from the rider. Working outside of the ring forces the rider to be conscious of all aids and to getting lazy by using the wall or fence as the outside aid, thus making the horse and rider communicate more effectively. If you have to work in the ring, NEVER work on the rail.