In the present paper, we take the leaf spring based double parallel-guiding mechanism (DPGM) as a particular case study to investigate a parametric model by considering the stress stiffening effect of the temperature variation based on the beam constraint model (BCM). In particular, a model with the temperature variation term of the DPGM is derived by incorporating the elastic stretch induced by the thermal effect of the leaf spring flexure into the BCM. Different from the traditional BCM, the compliance calculated by the established model is no longer only affected by the external loads, but the thermal deformation generated by the temperature variation. Therefore the derived model can describe both the load-nonlinearity and the thermal-nonlinearity. Based on the analysis results of a basic parallelogram module (BPM), we obtain a model of the DPGM, and the finite element analysis (FEA) method is adopted to verify the proposed model. The proposed model is a general parametric method to characterize the mechanical property of the DPGM, which can be further explored to support the optimization and control of motion systems composed of leaf spring based compliant mechanisms.