Here, we investigate supercritical heat transfer of CO2 in a 10.0 mm diameter horizontal tube, covering pressures, mass fluxes and heat fluxes in the ranges of (7.531∼20.513) MPa, (496.7∼1346.2) kg/m2s, and (97.4∼400.3) kW/m2, respectively. It is surprising to find the non-monotonic increase of wall temperatures along the flow direction. Besides, either positive or negative wall temperature differences, ΔT, exist between bottom tube and top tube. The three-regime-model is introduced to explore the mechanisms that trigger the above abnormal findings. The stratified-wavy flow involves a liquid-like (LL) core and a vapor-like (VL) layer on the tube wall. The wavy interface is formed by the two separated phases of LL and VL. The oscillation of wall temperatures is explained by the thermal conduction in the solid wall interacted with the stratified-wavy flow in the tube. Once wall temperatures increase, the local heat flux decreases to decrease the evaporation momentum force, reducing the VL layer thickness to ensure the heat transfer recovery. A regime map clarifies the positive and negative temperature difference runs, and the maximum wall temperature differences are well correlated based on the LL phase Reynolds number, ReLL,ave. In the two-phase-like (TPL) regime, the measured heat transfer coefficients significantly deviate from the predictions based on the single-phase fluid assumption. The strong deviation of hbot/htop from 1 indicates both important effects of pseudo-boiling and stratification in horizontal tubes, where hbot and htop are the heat transfer coefficients at the bottom generatrix and the top generatrix, respectively. Based on this work, the pseudo-boiling theory is recommended to deal with the supercritical heat transfer.