An analytical approximation for the two-dimensional heat conduction problem with temporally and spatially oscillating thermal boundary conditions is presented. In addition, simplified expressions for the damping and phase shift of the temperature signal between the surface and a measurement position inside the wall are derived and their validity in dependency on the inverse Fourier number is shown. The solution algorithm is implemented in a MATLAB program and made available for other researchers. In two case studies, the analytical solution is applied in order to evaluate the ability of experimental systems to measure instantaneous and local heat transfer coefficients as well as temperatures on a boundary.