  We determine the thermal evolution of the intergalactic medium (IGM) over
$3\, \mathrm{Gyr}$ of cosmic time $1.8<z<5.4$ by comparing measurements of the
Ly{\alpha} forest power spectrum to a suite of $\sim70$ hydrodynamical
simulations. We conduct Bayesian inference of IGM thermal parameters using an
end-to-end forward modeling framework whereby mock spectra generated from our
simulation grid are used to build a custom emulator which interpolates the
power spectrum between thermal grid points. The temperature at mean density
$T_0$ rises steadily from $T_0\sim 6000\, \mathrm{K}$ at $z=5.4$, peaks at
$14000\, \mathrm{K}$ for $z\sim 3.4$, and decreases at lower redshift reaching
$T_0\sim 7000\, \mathrm{K}$ by $z\sim1.8$. This evolution provides conclusive
evidence for photoionization heating resulting from the reionization of He II,
as well as the subsequent cooling of the IGM due to the expansion of the
Universe after all reionization events are complete. Our results are broadly
consistent with previous measurements of thermal evolution based on a variety
of approaches, but the sensitivity of the power spectrum, the combination of
high precision BOSS measurements of large-scale modes ($k\lesssim 0.02\,
\mathrm{s/km}$) with our recent determination of the small-scale power, our
large grid of models, and our careful statistical analysis allow us to break
the well known degeneracy between the temperature at mean density $T_0$ and the
slope of the temperature density relation $\gamma$ that has plagued previous
analyses. At the highest redshifts $z\geq5$ we infer lower temperatures than
expected from the standard picture of IGM thermal evolution leaving little room
for additional smoothing of the Ly{\alpha} forest by free streaming of warm
dark matter.
