Direct evidence of an inertial-range turbulent energy cascade has been provided by spacecraft observations in heliospheric plasmas. In the solar wind, the average value of the derived heating rate near 1 au is , an amount sufficient to account for observed departures from adiabatic expansion. Parker Solar Probe, even during its first solar encounter, offers the first opportunity to compute, in a similar fashion, a fluid-scale energy decay rate, much closer to the solar corona than any prior in situ observations. Using the Politano-Pouquet third-order law and the von Kármán decay law, we estimate the fluid-range energy transfer rate in the inner heliosphere, at heliocentric distance R ranging from 54 R (0.25 au) to 36 R (0.17 au). The energy transfer rate obtained near the first perihelion is about 100 times higher than the average value at 1 au, which is in agreement with estimates based on a heliospheric turbulence transport model. This dramatic increase in the heating rate is unprecedented in previous solar wind observations, including those from Helios, and the values are close to those obtained in the shocked plasma inside the terrestrial magnetosheath.