  We investigate the finite-temperature corrections to scaling in the
three-state square-lattice Potts antiferromagnet, close to the critical point
at T=0. Numerical diagonalization of the transfer matrix on semi-infinite
strips of width $L$ sites, $4 \leq L \leq 14$, yields finite-size estimates of
the corresponding scaled gaps, which are extrapolated to $L\to\infty$. Owing to
the characteristics of the quantities under study, we argue that the natural
variable to consider is $x \equiv L e^{-2\beta}For the extrapolated scaled gaps
we show that square-root corrections, in the variable $x$, are present, and
provide estimates for the numerical values of the amplitudes of the first-- and
second--order correction terms, for both the first and second scaled gaps. We
also calculate the third scaled gap of the transfer matrix spectrum at T=0, and
find an extrapolated value of the decay-of-correlations exponent,
$\eta_3=2.00(1)$. This is at odds with earlier predictions, to the effect that
the third relevant operator in the problem would give $\eta_{{\bf P}_{\rm
stagg}}=3$, corresponding to the staggered polarization.
