 Offer the dog water from the faucet, not ice water. Soak some towels with water from the faucet and have the dog lie on that. However, let's go back a bit, back outside. The dog may not have stopped playing or walking on its own and could soon show other more serious signs of a heat problem. Things to look for? A pet who is lethargic. Suddenly slow walking, may have trouble walking, staggering around, trying to walk.