Well I'm fairly sure alfalfa is the same as lucerne in Australia, so here goes.
I used to be a firm believer that it did not heat horses up. I'd never had an issue with it heating them, and that is with young breakers, ottb's, in particular a 3yr old ottb mare who was super hot, and various ponies, and cross breeds. Not one was heated on it, however in saying that all my horses are paddocked pretty much 24/7. The only time I yard them is before a competition, or due to an injury, and the only time they are stabled is before a major competition, a bad injury/illness or at a competion, so they do get lots of time to roam around.
I have thus far changed my opinion on his though, as I recently aquired a 20/21 year old tb gelding for my father he wants to learn to ride. This horse is very quiet in almost all aspects, but give him even just one biscuit of lucerne and he is a raving lunatic!!