A multiplicity of simulations is required to optimize systems with thermal transient processes in the presence of uncertain parameters. That is why model order reduction is applied to minimize the numerical effort. The consideration of heat radiation and convection with parameter-dependent heat transfer coefficients results in a nonlinear system with many inputs as these loads are distributed over the whole surface limiting the attainable reduced dimension. Therefore, a new input reduction method is presented approximating the input matrix based on load vector snapshots using singular value decomposition. Afterward, standard reduction methods like the Krylov subspace method or balanced truncation can be applied. Compared to proper orthogonal decomposition, the number of training simulations decreases significantly and the reduced-order model provides a high accuracy within a broad parameter range. In a second step, the discrete empirical interpolation method is used to limit the evaluation of the nonlinearity to a few degrees of freedom and proper orthogonal decomposition allows the fast adaptation of the emissivity. As a result, the reduced system becomes independent of the original dimensions and the computation time is reduced drastically. This approach enables an optimal method combination depending on the number of simulations performed with the reduced model.