MANY frogs don't need heat, and Axolotls LOVE cold water. Newts are ok in room temp, depending on the species. Turtles... many are good without heat. Mudskippers DO need heat.
I don't think so because none of the animals you listed are lizards, as the bet specified.
Also, name 3 freshwater turtles that are ideally suited for room-temperature (or cooler) water without any heating devices. I'll even give you the first one: any of the northernmost species of mud turtles.