A method for combining satellite altimetry observations with satellite measurements of the Earth's time-varying gravity to give improved estimates of the ocean's heat storage is presented. Over the ocean the time-variable component of the geoid can be related to the time-varying bottom pressure. The methodology of estimating the ocean's time-varying heat storage using altimetric observations alone is modified to include observations of bottom pressure. A detailed error analysis of the methodology is undertaken. It is found that the inclusion of bottom pressure improves the ocean heat storage estimates. The improvement comes from a better estimation of the steric sea surface height by the inclusion of bottom pressure in the calculation, over using the altimeter-observed sea surface height alone. On timescales of the annual cycle and shorter the method works particularly well. However, long-timescale changes in the heat storage are poorly reproduced because of deficiencies in the methodology and the presence of contaminating signals in the bottom pressure observations.