It is not strictly correct to state that loudspeaker impedance rises linearly with temperature. Only the resistive part of impedance due to the voice coil behaves this way.
Over most of the frequency range of a typical moving coil loudspeaker, the impedance is dominated by either the motional impedance caused by back-emf at low frequencies, or voice coil inductance at high frequencies. It is only essentially resistive in a narrow frequency range between these two, where it is largely determined by the voice coil resistance.
Any attempt to infer temperature by measuring current, must therefore take this into account (presumably by bandpass filtering the current sense signal).