This paper presents a new approach of meshless local B-spline based finite difference (FD) method for solving transient heat conduction problems in complex geometries with spatially non-homogeneous and time dependent heat sources. In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity for either field variable approximation or integration, hence truly meshless. Time integration is performed by using the Galerkin implicit scheme. Several transient heat conduction problems with non-uniform and localized heat sources having potential relevance in industrial applications are examined to demonstrate the efficacy of the present approach. Comparison of the method results with solutions from other numerical methods in literature is given. Good agreement with reference numerical methods is obtained and the presented new meshless local method is shown to be simple and accurate.