The Gemini Planet Imager (GPI) is a new facility, extreme adaptive optics (AO), coronagraphic instrument, currently being integrated onto the 8-meter Gemini South telescope, with the ultimate goal of directly imaging extrasolar planets. To achieve the contrast required for the desired science, it is necessary to quantify and mitigate wavefront error (WFE). A large source of potential static WFE arises from the primary AO wavefront sensor (WFS) detector's use of multiple readout segments with independent signal chains including on-chip preamplifiers and external amplifiers. Temperature changes within GPI's electronics cause drifts in readout segments' bias levels, inducing an RMS WFE of 1.1 nm and 41.9 nm over 4.44 degrees Celsius, for magnitude 4 and 11 stars, respectively. With a goal of <2 nm of static WFE, these are significant enough to require remedial action. Simulations imply a requirement to take fresh WFS darks every 2 degrees Celsius of temperature change, for a magnitude 6 star; similarly, for a magnitude 7 star, every 1 degree Celsius of temperature change. For sufficiently dim stars, bias drifts exceed the signal, causing a large initial WFE, and the former periodic requirement practically becomes an instantaneous/continuous one, making the goal of <2 nm of static WFE very difficult for stars of magnitude 9 or fainter. In extreme cases, this can cause the AO loops to destabilize due to perceived nonphysical wavefronts, as some of the WFS's Shack-Hartmann quadcells are split between multiple readout segments. Presented here is GPI's AO WFS geometry, along with detailed steps in the simulation used to quantify bias drift related WFE, followed by laboratory and on sky results, and concluded with possible methods of remediation.