We model the role of the ocean in climate change, using the concept of multicointegration. Surface temperature and radiative forcing cointegrate and the accumulated cointegration disequilibria represent the change in Earth system heat content, which is predominantly stored in the ocean. System heat content in turn cointegrates with surface temperature. Using a multicointegrating I(2) model, we find that the climate sensitivity is 2.8ºC and the rate of adjustment to equilibrium is realistically slow. These results contrast strongly with those from I(1) cointegration models and are more consistent with global circulation models. We also estimate Earth system heat content as a latent variable for the full period, 1850-2014, and this predicted heat content cointegrates with available ocean heat content observations for 1940-2014.