We generalize the state-of-the-art perturbative Equation of State of cold quark matter to nonzero temperatures, needed in the description of neutron star mergers and core collapse processes. The new result is accurate to order g^5 in the gauge coupling, and is based on a novel framework for dealing with the infrared sensitive soft field modes of the theory. The zero Matsubara mode sector is treated using a dimensionally reduced effective theory, while the soft non-zero modes are resummed using the Hard Thermal Loop approximation. This combination of known effective descriptions offers unprecedented access to small but nonzero temperatures, both in and out of beta equilibrium.

8 pages, 3 figures; v2: minor improvements, version published in PRL (without appendices)