We investigate how the strong coupling of a superconductor to thermal bosons can enhance its superconducting critical temperature. To tackle this problem, we use a renormalization group approach that allows us to describe the density fluctuations-induced attraction between fermions, capturing the mutual influence of bosonic and fermionic sectors. The self-consistent renormalization group framework predicts a robust increase of the critical temperature across a wide range of interactions. However, this enhancement is progressively suppressed as the system approaches the unitary limit, and therefore the intrinsic upper bound on the critical temperature of the unitary Fermi gas cannot be overcome. We find a nontrivial dependence of the critical temperature on the boson mass and we establish a phase diagram for enhanced superconductivity driven by bosons being either in the condensed or thermal state. We outline possible experimental realizations in cold atomic systems and discuss implementations using electron-exciton mixtures in van der Waals material heterostructures.