  We present new measurements of the temperature of the intergalactic medium
(IGM) derived from the Lyman-alpha forest over 2.0 < z < 4.8. The small-scale
structure in the forest of 61 high-resolution QSO spectra is quantified using a
new statistic, the curvature, and the conversion to temperature calibrated
using a suite of hydrodynamic simulations. At each redshift we focus on
obtaining the temperature at an optimal overdensity probed by the Lyman-alpha
forest, T(Delta), where the temperature is nearly a one-to-one function of the
curvature regardless of the slope of the temperature-density relation. The
median 2-sigma statistical uncertainty in these measurements is 8 per cent,
though there may be comparable systematic errors due to the unknown amount of
Jeans smoothing in the IGM. We use our T(Delta) results to infer the
temperature at the mean density, T0. Even for a maximally steep
temperature-density relation, T0 must increase from ~8000 K at z ~ 4.4 to
>~12000 K at z ~ 2.8. This increase is not consistent with the monotonic
decline in T0 expected in the absence of He II reionization. We therefore
interpret the observed rise in temperature as evidence of He II reionization
beginning at z >~ 4.4. The evolution of T0 is consistent with an end to He II
reionization at z ~ 3, as suggested by opacity measurements of the He II
Lyman-alpha forest, although the redshift at which T0 peaks will depend
somewhat on the evolution of the temperature-density relation. These new
temperature measurements suggest that the heat input due to the reionization of
He II dominates the thermal balance of the IGM over an extended period with
Delta_z >~ 1.
