This work extends our recently proposed design approach for hybrid solid-lattice structures to account for coupled thermal-mechanical loads. The conventional recursively defined multi-material interpolation model has been extended to describe both solid and gradient lattice materials. The extended model incorporates gradient control variables, treating the secondary "solid" material phase as a type of parameterized lattice. By means of numerical homogenization and interpolation, the effective mechanical and thermal behaviors of gradient lattices are explicitly expressed in terms of the gradient control variables, respectively. The extended design approach maintains the flexibility of customizing the variable range of gradient variables. Furthermore, a unified global volume constraint is incorporated in the thermal-mechanical scenario, resulting in the autonomous adjustment of material distribution between solid and lattice material phases. A series of benchmark design tests using two types of lattice materials validate the effectiveness of multi-material interpolation models that incorporate gradient material phases in thermal-mechanical design, ensuring the physical validity of intermediate-density regions and enhancing the manufacturability of the overall structure.