higher temperatures make the molecules move around faster and spread further apart.
water has a greater volume at a high temperature (it goes from liquid to gas form); but when water freezes at low temperatures it also expands (like when you freeze a plastic bottle of water and the plastic breaks).
The above answer is non-sense. It doesn't shed any light. When dealing with solids and liquids it is complicated. But it is quite simple for gases... here ya go:
The ideal gas law is:
PV = nRT, where P = pressure, V = volume, n= number of moles, R = ideal gas constant, T = Temperature in K