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Abstract What limits the value of the superconducting transition temperature (T c) is a question of great fundamental and practical importance. Various heuristic upper bounds on T c have been proposed, expressed as fractions of the Fermi temperature, T F, the zero-temperature superfluid stiffness, ρ s(0), or a characteristic Debye frequency, ω 0. 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 T c. To demonstrate this, we provide explicit models where T c/T F (with an appropriately defined T F), T c/ρ s(0), and T c/ω 0 are unbounded.