An approximate method for solving the transient boundary-value problem for a heat regenerator, based on expanding the Green function in a special bilinear, uniformly converging series is suggested. The solution is analyzed for error produced by retention of only one or two terms of the series, and an expression was obtained for calculating the temperature field of the regenerator matrix. It is shown that at Peclet numbers below one need only to retain a single term of the series for purposes of practical calculations.