I'd take him to a vet first.
How large is this savannah? Their diet should mostly consist of invertebrates not eggs, rats, and fish. These things are ok from time to time though.
Monitors are very active animals and if yours is sleeping for 75% of the day that really doesn't indicate very good health.
Keeping the animal in a room loose is not a good idea either, even with you keeping the room at 80-90F and putting in a basking light.
Go to the link provided by the above poster and make him a wooden cage that will contain heat and humidity properly.
Please post some pictures of both the animal and his living arrangements.