We decompose the Lyman- (Ly ) forest of an extensive sample of 75 high signal-to-noise ratio and high-resolution quasar spectra into a collection of Voigt profiles. Absorbers located near caustics in the peculiar velocity field have the smallest Doppler parameters, resulting in a low-b cutoff in the b- distribution set primarily by the thermal state of the intergalactic medium (IGM). We fit this cutoff as a function of redshift over the range , which allows us to measure the evolution of the IGM temperature-density ( ) relation parameters T0 and γ. We calibrate our measurements against mock Ly forest data generated using 26 hydrodynamic simulations with different thermal histories from the THERMAL suite, also encompassing different values of the IGM pressure smoothing scale. We adopt a forward-modeling approach and self-consistently apply the same algorithms to both data and simulations, propagating both statistical and modeling uncertainties via Monte Carlo. The redshift evolution of T0 (γ) shows a suggestive peak (dip) at z = 2.9 (z = 3). Our measured evolution of T0 and γ is generally in good agreement with previous determinations in the literature. Both the peak in the evolution of T0 at z = 2.8, as well as the high temperatures that we observe at 2.4 < z < 3.4, strongly suggest that a significant episode of heating occurred after the end of H i reionization, which was most likely the cosmic reionization of He ii.