This is an obsession of beer brewers. Books on beer thoroughly explain temperature cycles to be used for every kind of beer. (The craze of wine makers seems to be pH and moreover sulphite). As far as wine is concerned things look simple: cold for white (15-20°C/60-70°F), and warmer for red (25°C/80°F). Concerning mead... recommended fermentation temperatures vary greatly. Generally speaking, when in doubt wonder what is done to make white wine. It can help get an idea. So 15-20°C (60-70°F) it is.
What is the influence of temperature? If the temperature is low (but not below 15°C/60°F unless you have something special in mind and a suitable strain of yeast) fermentation will be rather slow. But this will also modify the balance between chemical equilibria, that is, proportions of various organoleptic compounds produced during fermentation will be different at different temperatures. And so will be the taste.
Fermentation is exothermic (it produces heat). If the vessel is small enough (high surface to volume ratio), heat will be easily dissipated. Otherwise, temperature must be monitored or else it may rise too much. This is especially true at the beginning of fermentation, when it is very active.
Except in some cases, some fortified wines for instance, temperature must be kept as stable as possible.