There are many knowledge gaps to be addressed in the behaviour of structural members under fire conditions. The behaviour of steel-concrete composite beams under the cooling phase is yet to be explored in-depth. In this paper, all the beam models are heated for an hour and the behaviour of composite beam systems in heating and cooling phases has been studied. The parameters considered for the present study are the axial stiffness of the supporting system of the composite beam and influence of the reinforcement at the support. A 3D finite element model of long span composite beam was developed using Abaqus software. The modelling technique and analysis procedure was validated with the literature. The length of the beam considered for parametric study was around 13 m. All models had simple shear connections. A parametric study was conducted to understand the influence of reinforcement at the beam ends, and the effect of support conditions provided for these reinforcements. The axial restraint provided at beam-ends were found to have a significant role in the behaviour of the beam under fire loading. Stiff connections are not preferable during the cooling phase of loading. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.