Keep him as moist as possible, anonymous. I know. That sounds a bit … odd, but that’s the simple truth. A toxicroak’s means of thermoregulation depends heavily on how moist its skin is. While toxicroak without the Dry Skin ability can generate a layer of mucus to trap some moisture in, those with Dry Skin have trouble producing this mucus. That’s why they need to be supplied with cool water: pools, frequent trips to the beach, plenty of water to drink, and so forth. The more hydrated your toxicroak is and the more your toxicroak bathes himself in water, the easier it will be for him to deal with the heat.
Of course, keeping him in a cool, perhaps air-conditioned place may help too.
Best of luck, anonymous!
The Pokédex According to Bill 