The multiquadric collocation method is a meshless method that uses multiquadrics as its basis function. Problems of nonlinear time-dependent heat conduction in materials having temperature-dependent thermal properties are solved by using this method and the Kirchhoff transformation. Variable transformation is simplified by assuming that thermal properties are piecewise linear functions of temperature. The resulting nonlinear equation is solved by an iterative scheme. The multiquadric collocation method is tested by a heat conduction problem for which the exact solution is known. Results indicate satisfactory performance of the method.