The oxygen in a tank will be used up by the fish, but the CO2 will gas off and oxygen will re-enter at the surface.
Assuming that the temperature of the water coming in and that of the tank is the same I suppose there might be a slight increase in the amount of dissolved gas, though this would be an extremely temporary effect (think of it lasting for seconds to a minute at most).
Colder water in would increase the amount of dissolved oxygen, but the level would return to normal once the water heats up.
So to answer, the change may cause a temporary fluctuation in O2 levels, but nothing major.
As to best view on heating or not. I think you will find most people who have a large number of larger tanks say no to heating as it is not necessary on most water changes (some members change large amounts and so have to).