I agree with putting some ice in the water bottle/crock so the water stays cool. Make sure to replace the water every day (you should do this anyways.) You might try having a water bottle and a crock, some buns prefer one over another. When you feed his daily veggies, leave a little extra water on them, that will automatically increase his water consumption. You might try getting some special grass hay blends like Orchard, Oat, Meadow, or Botanical. The more hay they eat, typically the more water they will drink.
My buns drink out of water bottles and what I will do is put about 2 inches of water in the bottle and put it. in the freezer The next day I fill it up with water and hang it in the pen. I take out the bottle from the previous day, rinse it out, fill with two inches of water, and put that one in the freezer. Obviously, you need two separate bottles to keep them rotating.
A big task will be keeping him cool. If you have air conditioning, as long as it’s comfortable in the house for you, he should be okay. Another way to keep it cool is to have blinds drawn so the hot sun is not shining on him during the day. You can have a fan and cover it with a damp sheet (don’t aim a fan directly on the bunny but use it to circulate the air).
That’s all I can think of right now… also a frozen water bottle or a cool ceramic tile to lay on…