Inverse heat conduction problems (IHCPs) are problems in which, based on known effects (e.g. temperature distribution or heat flux), unknown causes such as boundary conditions, heat sources or material properties are determined [1]. These problems are usually poorly conditioned from a mathematical point of view, which means that their solution is highly sensitive to measurement errors requiring the use of regularization methods. IHPs occur, among others, in thermal diagnostics, materials engineering, and biomedical engineering. Traditional numerical methods such as the boundary element method and the finite difference method have in the past been used for the solution of such problems, in combination with optimization and regularization techniques. More recently, the method of fundamental solutions (MFS) which is a meshless method has been employed used to solve the IHCPs [2]. In the MFS, a crucial issue is a choice of the source points. One of the techniques recently proposed in the literature for finding the optimal source location is the moving pseudo-boundary MFS [3]. In this approach, we treat both the coefficients in the MFS approximation and the source locations as unknowns to be determined as part of the solution and employ the standard MATLAB® routines lsqnonlin and fsolve to achieve this. We describe the application of the moving pseudo-boundary MFS for solving some examples of IHCPs, including backward heat conduction problems or identification of bioheat perfusion coefficients. Numerical results are also presented. References: [1] D. Lesnic, Inverse Problems with Applications in Science and Engineering, CRC Press, 2022. [2] J.A. Kołodziej, M. Mierzwiczak and M. Ciałkowski, Application of the method of fundamental solutions and radial basis functions for inverse heat source problem in case of steady-state, International Communications in Heat and Mass Transfer, Vol. 37(2), pp. 121-124, 2010. [3] J.K. Grabski and A. Karageorghis, Moving pseudo-boundary method of fundamental solutions for nonlinear potential problems, Engineering Analysis with Boundary Elements, Vol. 105, pp. 78-86, 2019.