I wouldn't be concerned about having hot water and ice in an ice catcher of the same bong, assuming it's of decent quality and glass thickness, and assuming you're not just putting large amounts of ice into boiling water. While I wouldn't say it's good for the bong's structural integrity, I would be surprised if someone's piece broke from temperature difference, rather than rapid temperature change, as is the case with the situation d16 described.

In terms of smoothness, as others have already mentioned, there are two factors: first, water vapor combines with smoke to give you more oxygen as you take the hit. This makes the smoke slightly less dense, but much easier on the lungs, perhaps allowing even bigger hits. I recall seeing bongs actually designed with small holes (cyclone I believe) to allow air in for the same purposes. The second factor, which I'm surprised hasn't been mentioned much, is more extensive filtration of carcinogens and harsh particles contained within the smoke. This is because with higher temperature, solubility increases, meaning the chemicals stay in the water, not in your lungs. This also means, however, that you may be losing more THC (not to mention other cannabinoids), as that too has higher solubility in conditions of high temperature. For this reason, I'd avoid boiling water - think cannabis tea - and stick to warm or hot.

Also, don't that more stuff in your water means more of a "bong water" effect, which is that much nastier if some of the water is evaporating, so you'll probably want to change your water between sessions.