Relay coil inductance variations vs. temperature
The inductance barely changes with temperature, as this is defined by the coils geometry, e.g. its dimensions and number of turns, you can think of it as the diameter and length of the coil will increase slightly, this changes the flux density at the ends of the coils slightly, 

the core material can shift slightly in relative permittivity, however both of these effects are below what most people are capable of measuring at home, 

The biggest change will come in the coil resistance increasing as temperature goes up, this is because coppers resistance per length increases with temperature, this changes the actuation and hold voltages slightly as you need a slightly higher voltage to get the same current through a higher resistance.