Nonlinear thermo-elastic buckling characteristics of composite variable stiffness beam with layers making use of curvilinear fibres under thermal environment is attempted here. The model is based on a shear deformable theory introducing trigonometric function, and considering von Kármán’s assumptions based geometrical nonlinear effect. The beam constitutive equation is modified according to the stress-free situation in the width direction of beam-Poisson’s effect in the formulation for predicting the behaviour of general lay-up composite beams. By the principle of minimum total potential energy, the governing equations in terms of incremental stiffness matrices are formed introducing general beam finite element. The global equilibrium equations formulated are solved for envisaging the post-buckling path through eigenvalue analysis iteratively, thus establishing the relationship of thermal temperature against moderate amplitude level of beam deflection. A systematic parametric analysis considering different lamina properties such as curvilinear fibre path angles and including lay-up sequences, thermal expansion coefficient, mixed laminate combining straight and curvilinear fibres-based layers is carried out on thermo-structural stability of curvilinear fibre-based beams. Also, the influence of geometric factors, flexible beam end support, and variation in thermal profile, etc. over the stability behaviour of beam is examined.