Why are DOM lithiations sometimes conducted at −78 °C and othertimes conducted at elevated temperatures?
The reason a given set of conditions used in any given reaction is likely fairly arbitrary unless you're following a paper where the conditions have been extensively optimised (for instance in an OPR&amp;D paper where a process group has rigorously screened) - as has been discussed here before, −78 °C  is a convenient temperature to run reactions, so if it works at −78 °C, its unlikely anyone will ever bother to warm it up. 

That said, in Clayden's Organolithiums: Selectivity for Synthesis (which is probably the most comprehensive reference of R–Li chemistry I can think of), a table of directing groups and representative conditions is presented. I've included the table below, but the actual text has a discussion of the various groups and a discussion of the representative conditions used. As a general guide, it seems that temperature is largely dictated by: 


the activating/deactivating nature of the directing group
the sterics of the directing group
the stability of the directing group, with low temperatures required in the case of electrophilic groups like the carbamate to prevent nucleophilic addition that would occur at higher temperature


As a general point, as temperatures get higher, the stabilisation of the anion by the directing group becomes less important to the overall energy and as such at higher temperatures, one would (generally) expect selectivity to drop. 



Summary of directing groups used in DoM reactions with typical reaction temperatures. Taken from Clayden, J. Organolithiums: Selectivity for Synthesis; Pergamon: Oxford, U.K., 2002; p 34.