Sim2,
Chemicals for print processing should ideally be the same. However, they do not always have to be at exactly 20°C. Warmer temperatures (as long as they don't go above 25°C or so) are fine. The developing times (and the reactions in the other chemicals) will be faster, but this usually doesn't present a problem, since papers are developed to completion. For repeatable results, use the factorial method of developing (note the time it takes for a specific mid-tone to emerge use that as a factor of the total developing time. Then, when developing the same print in the same developer at a different temp, you can simply note the emergence time, multiply be the factor and arrive at your (starting) developing time.)
Colder temperatures may work alright if close to 20°C, but much more than an degree or two may affect the activity of the developing agents differently and skew the activity/contrast characteristics of the developer (specifically, hydroquinone loses activity at lower temperatures).
That said, unless you are developing in a cold basement or garage where the temperatures are less than 18°C or so, you should be alright using room temperature for all your solutions.
What you do not want is a wide variation in solution temperatures (e.g., warm developer, cold stop and fix). While paper holds up to variations in temperature better than film, it is still not a good idea.
Hope this helps,
DoremusScudder
www.DoremusScudder.com