  The superconducting transition leads to a sharp resistance drop in a
temperature interval that can be a small fraction of the critical temperature
T$_c$. A superconductor exactly at T$_c$ is thus very sensitive to all kinds of
thermal perturbations, including the heat dissipated by the measurement
current. We show that the interaction between electrical and thermal currents
leads to a sizeable imaginary impedance at frequencies of order of tens of Hz
at the resistive transition of single crystals of the layered material
2H-NbSe$_2$. We explain the result using models developed for transition edge
sensors. By measuring under magnetic fields and at high currents, we find that
the imaginary impedance is strongly influenced by the heat associated with
vortex motion and out-of-equilibrium quasiparticles.
