Atomic-scale computational modeling of technologically relevant permanent magnetic materials faces two key challenges. First, a materials magnetic properties depend sensitively on temperature, so the calculations must account for thermally induced magnetic disorder. Second, the most widely-used permanent magnets are based on rare-earth elements, whose highly localized 4$f$ electrons are poorly described by standard electronic structure methods. Here, we take two established theories, the disordered local moment picture of thermally induced magnetic disorder and self-interaction-corrected density functional theory, and devise a computational framework to overcome these challenges. Using the new approach, we calculate magnetic moments and Curie temperatures of the rare-earth cobalt (RECo$_5$) family for RE=Y--Lu. The calculations correctly reproduce the experimentally measured trends across the series and confirm that, apart from the hypothetical compound EuCo$_5$, SmCo$_5$ has the strongest magnetic properties at high temperature. An order-parameter analysis demonstrates that varying the RE has a surprisingly strong effect on the Co--Co magnetic interactions determining the Curie temperature, even when the lattice parameters are kept fixed. We propose the origin of this behavior is a small contribution to the density from $f$-character electrons located close to the Fermi level.
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