Trade the alfalfa out for bermuda until you can get back to riding.
Legume hays are not a good thing to feed these easy keepers. Unless you will be schooling her really hard for some sort of event that involves catching a cow or for hunter/jumper, it might be a good idea to leave her off the alfalfa forever.
When you said she doesn't get any supplements except psyllium, does that mean she isn't getting any grain or other type of feed? It would help if she's not.
We have dropped down to the high 90's - 101. Everytime the weatherman says "it's going to nice today, high of 91", I think that means high of a 101 for me because I am 60 miles further south, which makes a huge difference where I live.
Hopefully this heat cycle will break soon and all of us can get back to our normal horse routines before the horses explode from lack of exercise