We need more detailed information in order to supply you with an intelligent answer. What is the grade of steel that you are considering, and over what temperature range will it be used?
Music wire is ASTM A228 and is only rated to 250 degree F when used in its hardened state for springs.
Music wire is also used in its annealed stated for cutting foam but there are better choices if this is what you are doing. Foam cutting temperature should be less than 300 degree F.
I would guess it would be in the range of 7-10 millionth inch per degree F and fairly linear to around 550 degree F. You should be able to get much better numbers from the supplier.
Unless you are designing a spring with extremely accurate properties, I do not think that you have to account for thermal contraction/expansion of the music wire with reference to the spring force/deflection.
Compression springs are usually specified with +/-10% tolerance on the force in a specified deflection.
There is an alloy C-SPAN (I think) that has a constant elastic modulus over a wide range of temperatures which is usually what bother designers of very accurate springs but not the expansion contraction of the wire.
