Interesting idea, I am all for "keeping it simple", and if it works for you, fine!
I am sure that this will keep dust down, and the warmth will release the aromas and generally make the hay more palatable. I'm not convinced, though, that it would definitely be enough to kill all the spores in...
Here's one I made earlier.
https://www.youtube.com/watch?v=nPHwPgHuRfo
Originally I made a single one, using a 360 litre wheelie bin. I found I needed to line it with insulation to reach the required temperature of 80 degrees C (180 F). Then I was asked to make a second one, and in fact...
Looking for a source in the Dursley area. Can collect small bales in horsebox, or looking for delivery of four large bales. This is for feeding mules, so *must* be barley, please.