I'm not a vet or qualified to say. But I'm willing to take a guess.
Seems like edema like that could be related to a heart problem. He's lethargic, the swellings could indicate circulation problems. Did your vet listen to his chest to see if he could detect a murmur or something. If you have heart issues, heat could really sap you and make swelling worse. I'm totally guessing, of course.
I've just not really seen that kind of swelling in multiple places. Sometimes a bug bite will cause a strong local reaction around the site, and legs swell up from poor circulation when a horse is confined, but if he's older and swelling on lower portions (below his heart) that's all I can think of..the heart isn't working well enough to keep all his fluids moving. I'd keep him cool and hydrated, maybe provide a fan but not confine him, but definitely not force any exercise. Ask your vet about heart issues just to be sure.
Hopefully someone here will recognize the symptoms and can offer better advice?