The efficacy of ligation is a trade off between kinetic energy and enzyme activity. At lower temperatures there is reduced molecular motion, thus there is a greater occurrence of compatible molecules being positioned correctly, and for long enough, for the ligase to ligate. Needless to say that at lower temperatures the ligation rate is reduced, thus necessitating extended ligation times. Clearly, at elevated temperatures, the enzyme will be more active, but the efficacy of ligation is reduced as a product of both increased unstable contacts between the compatible fragments, and reduced enzyme stability.

Additional trade offs come from potential exonuclease activity, where extended incubation times, or more optimal (raised) temperatures using higher concentrations of ligase may result in removal of overhanging terminal nucleotides. In most commercial preparations however, this is negligible.

You have to decide what temperature is practical for your needs. Ligations are not universally performed at 4 degrees as it very much depends on the melting temperature of the overhangs that you are trying to ligate (Ferretti & Sgaramella, 1981). Clearly long, GC rich overhangs are going to have a much higher melting temperature than short AT overhangs (or blunt ends), thus can achiev stable interactions at higher temperatures.

In addition, we frequently don’t have the time to perform ligations at 4 degrees, as they take too long. Often 14-16 degrees is used in a 16 hr incubation (this is usually, but not universally, recommended for blunt end ligations) with the addition of molecular crowding agents, such as polyethylene glycol (PEG), which effectively reduces the aqueous volume in which macromolecules can interact, thus increasing the chance (a duration) of them interacting (though you should note that if you incubate at too lower temperatures with PEG, or increase the [PEG], then you could precipitate your DNA, which is no good for ligation!).

For sticky ends, most users get away with a 1 hour ligation at room temperature. They increase the fidelity of ligation by using much higher concentrations of ligase and also with much higher concentrations of PEG.

Hope that helps.