What is the relationship between temperature and volume
First, it depends on the substance.
For an ideal gas, temperature, volume, pressure satisfy the ideal gas equation of state PV is equal to nRT. If P is constant, then obviously for a given amount of gas, V is proportional to T.
For liquids and solids, the effect of pressure is not significant (not extreme) and is generally not considered. The common phenomenon is "thermal expansion and cold contraction", for specific conditions, some substances will also appear anti-expansion phenomenon. In calculation, the thermal expansion coefficient is usually used to represent the relationship between volume and temperature.