What role does temperature play in the type of precipitation that develops?

Above 30 degrees farenhieit or 0 degrees celcius there would be rain below there would be snow

Warm air holds more moisture than cold air. When the air has reached "saturation point" (it cannot hold any more moisture), it is more likely to cause precipitation as the over saturated air forms moisture droplets that fall as precipitation. 

One of the major causes of precipitation is when warm air cools rapidly (for example, when it rises after hitting a mountain front or other landmass). As the warm air cools, it loses its ability to retain moisture and becomes saturated, thus creating precipitation. We learned this in science class. :p hope this helps