The thermo-hydraulic characteristics of heated supercritical CO2 (SCO2) flows are investigated numerically in a vertical pipe from first- and second-law perspectives, and the influence of the flow direction, mass flux and heat flux (both distribution and average value) are evaluated. Two mass flux (254 kg/(m2∙s) and 400 kg/(m2∙s)) and three average heat flux (30 kW/m2, 50 kW/m2 and 70 kW/m2) conditions are simulated at an inlet temperature of 288 K and a pressure of 8.0 MPa (corresponding pseudo-critical temperature of 308 K) in a 4-mm diameter pipe. The simulation results reveal that the heat transfer is enhanced and the irreversibility is reduced in downward flows relative to flows without gravity, whereas the heat transfer deteriorates and the irreversibility is increased in upward flows. Both higher heat fluxes and lower mass fluxes also further hinder heat transfer in the upward flows, and multiple peaks are observed in the axial wall temperature profile. Moreover, it is found that the heat-flux distribution has a significant effect on the heat transfer performance of upward flows; the heat transfer further deteriorates and the irreversibility is further increased when a linearly decreasing heat-flux distribution is applied to the wall, while the heat transfer deterioration is alleviated when a linearly increasing heat-flux distribution is used. An analysis of the heat transfer mechanism indicates that the turbulence production in the core region of the supercritical flow is suppressed, and the accumulation of gas-like fluid in the near-wall region is promoted by the buoyancy effect in upward flows, leading to severe heat transfer deterioration and a sharp increase in the wall temperature, which is similar to the critical heat-flux phenomenon in subcritical boiling. The present study provides insights into the heat transfer characteristics of SCO2 flows, as well as practical guidance on the design and optimisation of relevant components and equipment.