Neutron stars and their mergers provide the highest-density regime in which Einstein's equations in full (with a matter source) can be tested against modified theories of gravity. But doing so requires a priori knowledge of the Equation of State from nuclear and hadron physics, where no contamination from computations of astrophysics observables within General Relativity has been built in. We extend the nEoS uncertainty bands, useful for this very purpose, to finite (but small) temperatures up to 30 MeV, given that the necessary computations in ChPT and in pQCD at already available in the literature. The temperature-dependent band boundaries will be provided through the COMPOSE repository and our own website.