It really depends on the fish. Trout do best in cool, fast running streams with lots of oxygen. Catfish like the warm, slow moving areas that may not have a lot of oxygen. The fish that people keep as pets have many different needs too.

You can see how fast a fish is breathing by watching the gill cover(operculum) move. You will see that they breathe faster in warm water.One reason is that warm water holds less oxygen. Another is that the warmer water will speed up the metabolism of the fish, which means they need more oxygen.

The good news is that putting too much oxygen in the water won't hurt the fish, so if you're concerned that your fish isn't getting enough oxygen, you can put a simple aerator in the tank to bubble air into the water.

You can also read up on your fish to see what its specific needs are.This site:
click_here
has a pretty long list of fish that you might have.

If your fish needed more oxygen than it was getting, and you added an aerator to its tank, would its breathing rate increase or decrease?

Unfortunately to answer this question, I would have to know which species offish you are talking about.At least for b) temperature is very related to the species. Tropical fish require a much warmer environment than say an arctic fish. If this is concerning aquarium fish, most stores sell fish that do best around 74 - 78 deg F although some fish (like goldfish and betas) do well at a temperature as low at 40 degF.

Colder water tends to have a higher dissolved oxygen than warmer, tropical waters. So an aquarium with a warmer environment should not contain as many fish as a cooler tank.

If you have a specific species or environment in mind, please let scienceline know and I will try to get a more specific answer for you.

a. Typical water that is agitated by the atmosphere should generally be good, if the water temperature is what the fish is used to; oxygen is less soluble in warmer water.

b. Depends on the fish - a tropical reef fish will like tropical water. Arctic Char like water that is close to freezing.