Selective laser melting (SLM) wherein a metal part is built in a layer-by-layer manner in a powder bed is a promising and versatile way for manufacturing components with complex geometry. However, components built by SLM suffer from substantial deformation of the part and residual stresses. Residual stresses arise due to temperature gradients inherent to the process and the accompanying deformation. It is well known that the SLM process parameters and the laser scanning strategy have a substantial effect on the temperature transients of the part and henceforth on the degree of deformations and residual stresses. In order to provide a tool to investigate this relation, a semi-analytical thermal model of the SLM process is presented which determines the temperature evolution in a 3D part by way of representing the moving laser spot with a finite number of point heat sources. The solution of the thermal problem is constructed from the superposition of analytical solutions for point sources which are known in semi-infinite space and complimentary numerical/analytical fields to impose the boundary conditions. The unique property of the formulation is that numerical discretisation of the problem domain is decoupled from the steep gradients in the temperature field associated with localised laser heat input. This enables accurate and numerically tractable simulation of the process. The predictions of this semi-analytical model are validated by experiments and the exact solution known for a simple thermal problem. Simulations for building a complete layer using two different scanning patterns and subsequently building of multiple layers with constant and rotating scanning patterns in successive layers are performed. The computational efficiency of the semi-analytical tool is assessed which demonstrates its potential to gain physical insight in the full SLM process with acceptable computational costs.