This article addresses the lack of heat transfer inversion analysis algorithms for current-bearing heat treatment furnaces. A one-dimensional unsteady heat conduction equation is used as the heat transfer mathematical model, and the quantum particle swarm stochastic optimization algorithm (QPSO) is employed to invert the heat transfer coefficient in the inverse heat conduction problem (IHCP) with the addition of random noise. In algorithm simulation experiments, the QPSO optimization algorithm exhibited high accuracy in solving the inverse problem of heat conduction. Meanwhile, with the addition of the wavelet filtering algorithm, the noise resistance of the inversion algorithm was significantly improved.