
Unless it is a really tiny bowl, if you are needing to refill it three times it sounds to me more like your pup has gotten into a habit; rather than actually being that thirsty. If the heating was making him extra thristy he would be drinking more throughout the day; not just in the evening.
If you are feeding him dry food I would try soaking it in a bit of warm water for his last meal of the day, which should cut down any real need for lots of extra water. Even if wet, I would add a small amount of water.
I would also give him only a small amount of water in the bowl in the evening last thing before his bedtime for a couple of days, regardless of barking for more. If he does not drink more water than normal in the morning than his excess drinking in the evening was out of habit, and not need.
One of my dogs always has a drink after he comes in from his last garden visit of the evening, it's definitely a habit, but for him its just a quick drink and not to excess.