Temperature DOES affect precipitation.
More Info: Surface temperature affects the rate of evaporation, which has a direct effect on cloud formation. Also, changes of temperature within the atmosphere determine what form precipitation takes as it falls to the ground (1).
Formation of Precipitation
Precipitation begins when heat from the sun evaporates water from Earth’s surface. Water will continue to evaporate until the local atmosphere reaches total saturation. How much moisture the atmosphere can hold is a function of temperature: warm air can hold more water vapor than cold air (2). Evaporated water will often form into a cloud, but not all clouds lead to precipitation. Clouds which form at the highest altitudes are often too cold for liquid water to form. A cloud will only produce precipitation within a narrow band of temperatures where liquid water can condense and coalesce (3).
Kinds of Precipitation
Precipitation can take many forms including rain, sleet, snow, freezing rain, and hail. Which type of precipitation reaches the ground is determined by variations in air temperature with altitude. If the entire atmosphere between the cloud and ground is above freezing, precipitation takes the form of rain. Snow occurs when atmospheric temperature is entirely below freezing. Sometimes, the atmosphere will have multiple temperature layers, some that are below freezing and some that are above freezing. In this scenario, precipitation which begins as snow will melt and refreeze, causing hail, sleet or freezing rain. Likewise, precipitation which begins as rain can freeze if it passes through freezing temperatures before reaching the ground (5).
(1) “Precipitation.” NWS JetStream –. N.p., n.d. Web. 23 Jan. 2013. <http://www.srh.weather.gov/srh/jetstream/synoptic/precip.htm>.
(2) “Effects of Changing Climate.” National Center for Atmospheric Research. N.p., n.d. Web. 23 Jan. 2013. <http://www.cgd.ucar.edu/cas/Trenberth/GLOB_CHANGE/extremes.html>.