What limits the value of the superconducting transition temperature (Tc) is a question of great fundamental and practical importance. Various heuristic upper bounds on Tc have been proposed, expressed as fractions of the Fermi temperature, TF, the zero-temperature superfluid stiffness, ρs(0), or a characteristic Debye frequency, ω0. We show that while these bounds are physically motivated and are certainly useful in many relevant situations, none of them serve as a fundamental bound on Tc. To demonstrate this, we provide explicit models where Tc/TF (with an appropriately defined TF), Tc/ρs(0), and Tc/ω0 are unbounded. © 2022, The Author(s).