Changes in ocean heat content are a critical element of climate change, with the oceans containing about 90% of the excess heat stored in the climate system (60% in the upper 700 db). Estimates of these changes are sensitive to horizontal mapping of the sparse historical data and errors in eXpendable BathyThermograph data. Here we show that they are also sensitive to the vertical interpolation of sparsely sampled data through the water column. We estimate, using carefully constructed vertical interpolation methods with high-quality hydrographic (bottle and CTD) data, the observationally based upper ocean heat content increase (thermosteric sea level rise) from 1956 to 2020 is 285 Zeta Joules (0.55 mm yr^-1), 14% (14%) larger than estimates relying on simple but biased linear interpolation schemes. The underestimates have a clear spatial pattern with their maximum near 15ºN and 12ºS, near the maxima in the curvature of the temperature depth profile.