  We compute robust lower limits on the spin temperature, $T_{\rm S}$, of the
$z=8.4$ intergalactic medium (IGM), implied by the upper limits on the 21-cm
power spectrum recently measured by PAPER-64. Unlike previous studies which
used a single epoch of reionization (EoR) model, our approach samples a large
parameter space of EoR models: the dominant uncertainty when estimating
constraints on $T_{\rm S}$. Allowing $T_{\rm S}$ to be a free parameter and
marginalizing over EoR parameters in our Markov Chain Monte Carlo code 21CMMC,
we infer $T_{\rm S}\ge3 {\rm K}$ (corresponding approximately to $1\sigma$) for
a mean IGM neutral fraction of $\bar{x}_{\rm H{\scriptsize I}}\gtrsim0.1$. We
further improve on these limits by folding-in additional EoR constraints based
on: (i) the dark fraction in QSO spectra, which implies a strict upper limit of
$\bar{x}_{\rm H{\scriptsize I}}[z=5.9]\leq 0.06+0.05 \,(1\sigma)$; and (ii) the
electron scattering optical depth, $\tau_{\rm e}=0.066\pm0.016\,(1\sigma)$
measured by the Planck satellite. By restricting the allowed EoR models, these
additional observations tighten the approximate $1\sigma$ lower limits on the
spin temperature to $T_{\rm S} \ge 6$ K. Thus, even such preliminary 21-cm
observations begin to rule out extreme scenarios such as `cold reionization',
implying at least some prior heating of the IGM. The analysis framework
developed here can be applied to upcoming 21-cm observations, thereby providing
unique insights into the sources which heated and subsequently reionized the
very early Universe.
