This work aims to introduce a general formulation of topology optimisation (TO) problems involving design-dependent loads (DDLs) resulting from thermomechanical analysis in the framework of a special density-based TO method. This approach is based on non-uniform rational basis spline (NURBS) entities to represent the topological descriptor, which guarantee the continuity of the pseudo-density field, the CAD compatibility of the solution and, thanks to the local support property, an implicit filtering action to reduce the mesh dependency and the checkerboard effect. When considering DDLs, the boundary of the structure evolves along the optimisation process changing consequently the location, magnitude and orientation of the applied load, introducing different issues in the TO problem compared to the design-independent TO problems. The effectiveness of the method is proven on both 2D and 3D problems considering the classical expression of the thermomechanical loads taken from the literature. Firstly, a sensitivity analysis aimed at study the influence of the penalisation schemes combination is performed. Successively, the influence of the integer parameters of the NURBS entity, and the nature of thermomechanical loads on the optimised solution is considered. Finally, a more general formulation involving an exact integration of the temperature field over the element is introduced to achieve better optimised solutions.