Among additive manufacturing techniques, fused deposition techniques, which includes Fused Deposition Modelling (FDM) or Free Form Extrusion (FFE) are one of most popular due to its easy operation, utilization of environmentally safe materials and reproducibility. The performance of parts produced by these techniques depends mainly on their dimensional accuracy, surface quality and mechanical performance. These attributes are strongly influenced by the evolution of the filament temperature and deformation during deposition and solidification. In practice, each filament should solidify as quickly as possible to avoid excessive deformation due to gravity and/or due to the weight of the material deposited above it, and simultaneously, should remain sufficiently hot during enough time to ensure adequate bonding with the neighbouring filaments. Thus, the availability of adequate process modelling would offer a powerful tool to find an adequate solution to the conflicting pre-requisites, to support efficient process set-up and optimization. This work presents a computer solution for transient heat transfer during filament deposition, which involves the resolution of the energy balance equation taking into account all the relevant contacts between filaments as the deposition takes place (conduction with support and between adjacent filaments and between the filaments and the surroundings) coupled to a healing criterion. It is then shown that taking into consideration the material properties and process variables the develop tool can be used to estimate the influence of the main process parameters on adhesion and thus assist operation set-up and/or optimization.