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Within the environmental context, numerical modeling is a promising approach to assessing the energy efficiency of buildings. Resilient buildings need to be designed, and capable of adapting to future extreme heat. Simulations are required assuming a one-dimensional heat transfer problem through walls and a simulation horizon of several years (nearly 30). The computational cost associated with such modeling is quite significant and model reduction methods are worth investigating. The objective is to propose a reliable reduced-order model for such long-term simulations. For this, an alternative model reduction approach is investigated, assuming a known Proper Orthogonal Decomposition reduced basis for time, and not for space as usual. The model enables computing parametric solutions using basis interpolation on the tangent space of the \textsc{Grassmann} manifold. Three study cases are considered to verify the efficiency of the \revision{reduced-order} model. Results highlight that the model has a satisfying accuracy of $10^{\,-3}\,$ compared to reference solutions. The last case study focuses on the wall energy efficiency design under climate change according to a \revision{four-dimensional} parameter space. The latter is composed of the load material emissivity, heat capacity, thermal conductivity, and thickness insulation layer. Simulations are carried over $30$ years considering climate change. The solution minimizing the wall work rate is determined with a computational ratio of $0.1\%$ compared to standard approaches.