  Despite its importance for modeling the homogeneous hot early universe very
little is experimentally known about the magnitude of the reheating
temperature, leaving an uncertainty of remarkable 18 orders of magnitude. In
this paper we consider a general class of polynomial inflaton potentials up to
fourth order. Employing a Monte Carlo scan and imposing theoretical and
experimental constraints we derive a robust lower limit on the energy scale at
the end of inflation, $V_\text{end}^{1/4} > 3 \times 10^{15}$ GeV for sizable
tensor modes, $r \geq 10^{-3}$. If the reheating phase is perturbative and
matter dominated, this translates into a lower bound on the reheating
temperature, yielding $T_\text{rh} > 3 \times 10^8 \; (7 \times 10^2)$ GeV for
gravitational inflaton decay through a generic dimension five (six) operator.
