Modern precise radial velocity spectrometers are designed to infer the existence of planets orbiting other stars by measuring few-nm shifts in the positions of stellar spectral lines recorded at high spectral resolution on a large-area digital detector. While the spectrometer may be highly stabilized in terms of temperature, the detector itself may undergo changes in temperature during readout that are an order of magnitude or more larger than the other optomechanical components within the instrument. These variations in detector temperature can translate directly into systematic measurement errors. We explore a technique for reducing the amplitude of CCD temperature variations by shuffling charge within a pixel in the parallel direction during integration. We find that this “dither clocking” mode greatly reduces temperature variations in the CCDs being tested for the NEID spectrometer. We investigate several potential negative effects this clocking scheme could have on the underlying spectral data.