The present study evaluates the effect of heat treatment on electrospun poly(lactide-co-glycolide) fibrous membranes. Both a temperature (75–150 °C) and a treatment time range (5–40 min) are tested. The effect on the fibrous structure is investigated in terms of morphology, showing that with increasing temperature or longer treatment time the fusion of fibres progresses continuously. Additionally, the tensile properties of the various scaffolds deliver results on the effect of increasing fibre-to-fibre linkages. Both modulus and yield increase within the heat treatment procedures. The elevated stiffness of the membranes accompanies a loss in porosity. These findings deliver insights into the tailoring of membranes that might be used in the fabrication of customised scaffolds intended for cell culture in tissue engineering.