measure temperature in a solenoid without sensot
Yes, you can estimate the change in temperature of the copper windings of a solenoid, by measuring their resistance. The tempco of resistance for copper is about +10% for every 25C rise. You can get accurate values from a resource like Kaye and Laby online, here.

If your driving source is sensitive to the resistance, then yes, your waveform will change slightly. If it is a high output impedance current source, then no, the waveform will not change with changes in resistance.

Other parameters like the expansion due to temperature affecting the self inductance or capacitance will be pretty negligible, unless you make very sensitive measurements.