The hydrodynamic regime has a significant impact on the convective heat transfer for high-speed flows. Low Reynolds numbers and moderate flow accelerations lead to decrease of turbulent heat transfer rate due to flow laminarization. These flow conditions are typical for gas turbine blades and supersonic nozzles. Acceleration violates the Reynolds analogy, reduces the thickness of the dynamic boundary layer and has no effect on the thermal one. The latter statement allows us to use the thermal characteristics of the flow to estimate the intensity of the laminarization process. Experimental studies of heat transfer in a turbulent accelerating boundary layer under laminarization conditions were carried out in the paper. The regimes were studied, in which values of flow acceleration parameter K reached K=1‑4·10^-6. These values are typical for laminarization in the channel. Various channel geometries with flow acceleration at different lengths and different stagnation pressure in plenum were investigated to estimate the effect of acceleration intensity on the flow. The transient heat transfer method was implemented for estimation of heat transfer coefficient and adiabatic wall temperature. A decrease in the relative heat transfer coefficient St_exp/St_turb was found. St_exp/St_turb value dropped to values corresponding to the laminar boundary layer as the gas moved downstream in the acceleration region. However, this decrease was practically independent of the K value.