  We calculate the upper bound on the reheating temperature given the
non-observation of gravitational waves if the number of efolds during inflation
are the minimum number required to address the horizon problem as formulated in
terms of entropy. This bound is valid for canonical single field slow roll
inflation with a generic potential. Our bound numerically is
$T_{\text{reh}}\lesssim1.7\times10^{13}$ GeV, which is a factor of 428 less the
usual bound one obtains from the non-observation of gravitational waves alone.
If inflation lasted much longer than the minimum number of required efolds, our
bound relaxes to coincide with the usual bound. We discuss the relevance for
studies of primordial black holes.
