This work describes the implementation and evaluation of the Slab Ocean Model component of the Energy Exascale Earth System Model version 2 (E3SMv2-SOM), and its application to understanding the climate sensitivity to ocean heat transport (OHT) strength and CO$_{2}$ forcing. E3SMv2-SOM reproduces the baseline climate and Equilibrium Climate Sensitivity (ECS) of the E3SMv2 fully coupled experiments, reasonably well, with a pattern correlation close to 1 and global mean bias that is less than 1$\%$ of the fully coupled surface temperature, precipitation and sea ice extent and volume. Similar to other model behaviour, the ECS estimated from the SOM (4.5$^\circ$C) is greater than the estimate from fully coupled model (4.0$^\circ$C; from 150 years regression). The E3SMv2 baseline climate is also very sensitive to the strength of the OHT from which the prescribed ocean heat convergence (OHC) for the SOM is derived, with a surface temperature difference of about 4.0$^\circ$C between high- and low-OHT SOM experiments. The surface temperature response in the high/low-OHT experiments occur through a positive/negative Shortwave cloud radiative effect, caused by a decrease/increase in marine low-level clouds over subpolar regions. This surface temperature sensitivity to prescribed OHCs is particularly large in the Southern hemisphere and is associated with an overcompensation of between prescribed OHC/OHT by atmosphere heat transports. This large sensitivity indicates stronger low-level cloud feedbacks in E3SM. The SOMâ\euro™s ECS estimate is also sensitive to the baseline climate it is initialized from, with an ECS difference of 0.5$^\circ$C between the high- and low- OHT CO$_2$ increase experiments.