A fast and accurate procedure is proposed for solution of the twodimensional unsteady heat conduction equation used in the transient short-hot-wire method for measuring thermal conductivity. Finite Fourier transforms are applied analytically in the wire-axis direction to produce a set of one-dimensional ordinary differential equations. After discretization by the finite-volume method in the radial direction, each one-dimensional algebraic equation is solved directly using the tridiagonal matrix algorithm prior to application of the inverse Fourier transform. The numerical procedure is shown to be very accurate through comparison with an analytical solution, and it is found to be an order of magnitude faster than the usual numerical solution.