The line-of-sight power spectrum (P_F(k)) of the Ly-α forest has proven to be a valuable tool for doing cosmological observations. It also not only allows to constrain cosmological parameters, but enables us to measure the thermal state of the IGM at redshifts z>1.8. While at large scales (k<0.02 s/km) P_F(k) has been accurately measured using the large number (10^3-10^5) of quasar sightlines from SDSS and BOSS, there are much less spectra available at smaller scales (larger k). Prior power spectrum measurements from high-resolution data only used several times less (QSO) spectra in our redshift range about 15 years ago whereas a few hundred became available in the meantime. We therefore performed a new measurement using 74 quasar sightlines with 1.8<z<3.4 significantly improving the precision of the small-scale P_F(k). Using this additional precision on small scales combined with the BOSS measurements on large scales enables us to accurately constrain the thermal cutoff scale of the IGM set by a combination of temperature broadening of Ly-α forest lines, and ‘Jeans’ smoothing due to baryonic pressure support. We perform an MCMC analysis based on Gaussian process based techniques for interpolation between a grid of high-resolution hydrodynamical simulations and using our new high-resolution dataset, the BOSS data, a recent X-SHOOTER analysis, and a previous HIRES/MIKE analysis at higher redshifts. This allows us to measure thermal evolution in the IGM from z=5.4 to z=1.8 showing a suggestive peak at z~3.3 that might be attributed to He reionization. These constraints will help solving the existing discrepancies in the IGM thermal evolution between different works using different techniques as existing degeneracies between different thermal parameters in the existing measurements can be broken in our analysis.and can be used to place limits on possible exotic sources of heating. Additionally a better knowledge of thermal evolution will also lead to better constraints of e.g. the nature of dark matter or neutrino masses by breaking degeneracies in those measurements and thereby improve our knowledge of the underlying cosmology.