Unless there is a risk that the water might freeze over, yes, a heater is bad.
Get him out of the water!!! He will drown! He can live outside the water and won't drown.!!!!
Nonsense! It can drown under water if the oxygen concentration is too low and it's unable to reach the surface to gulp air as supplementation, yes, that's a possibility. However it
cannot live outside the water for any significant amount of time. The moment the skin and the gills start to dry out, the animal is in serious trouble.
The best course of action is definitely what Slowfoot recommended, a shallow enough container that the animal can gulp air with minimum effort but never have any of its parts outside of the water.
As well as reading the caresheet Slowfoot provided, you should give a thorough read to the water quality and cycling articles, the way your tank is set-up you are likely to experience problems with water quality. Also, you should start reading as many threats as possible. There's an unbelievable amount of info on aquatic ambystomatids in this site.
In the future, i would encourage you to not participate of the wild-caught market, the animal you have in your house was taken from the wild, stacked with many others, imported in bad conditions, stored and exposed to who knows what....the survivors are then delivered to shops where they almost always receive inadequate care, undergo no quarantines or anything, etc, then sold to you. This is both bad for the species, bad for the animals in question and bad for you as a costumer. It's bad in every permutation.
