What factors affect daily temperature range?
There are a lot of aspects affecting daily temperature. I want to distinguish between factors, which may change from day to day and others which are fixed and thus affect more the annual cycle of temperature (like altitude of place).

Some factors which affect daily temperature and change daily:


prevailing winds (temperature/moisture advection)
cloudiness
day of the year: duration of day (and thus insolation) is important for daily temperature range. The longer sun shines, the more solar radiation is absorbed by surface and the higher temperatures you get. For example, during equinox (march and september) day and night have the same duration and you have the longest or shortest day during solstice (in June and December). Thus this aspect is more relevant at middle and high latitudes.  


Other aspects which do not change daily:


local relief and surface type (atmosphere is heated due to absorption of solar radiation by surface)
distance to ocean/large lake (maritime vs. continental climate)
latitude: the angle of incidence of solar radiation changes with latitude (and day of the year)