The thermohydraulic characteristics of supercritical CO2 flows in a vertical tube at cooling conditions are numerically investigated, and the influence of the heat-flux condition and of the flow direction are evaluated. Constant (i.e., uniform), linearly increasing and linearly decreasing heat-flux conditions are considered as three typical heat-flux distributions over the pipe length. The simulation results show that there exists a maximum heat transfer coefficient at all heat-flux conditions when the fluid bulk temperature is slightly higher than the pseudo-critical temperature, but also that the heat-flux condition has little effect on the peak value of the heat transfer coefficient. From the viewpoint of the second law of thermodynamics, the influence of the heat-flux condition on the local entropy generation can be attributed to the distributed matching between the heat flux and the difference between the wall temperature and the fluid bulk temperature, as a better matching is associated with a higher uniformity of the local entropy generation and reduced overall irreversibilities. Upward and downward flows are considered, along with flows without gravity as a baseline case for comparison purposes, with the field synergy principle employed to explain the different phenomena in these flows. The buoyancy effect laminarises the downward flows and raises the temperature gradient; hence, the heat transfer deteriorates and the irreversibility increases. In the upward flows, the buoyancy effect augments the turbulence and alleviates the variations in temperature and velocity in the core region, consequently reducing the irreversible loss and enhancing heat transfer. The present study provides insights into the mechanisms of supercritical CO2 heat transfer characteristics as well as practical guidance on the design and optimisation of relevant components.