Surveys of nearby field stars indicate that stellar binaries are common, yet little is known about the effects that these companions may have on planet formation and evolution. The Friends of Hot Jupiters project uses three complementary techniques to search for stellar companions to known planet-hosting stars: radial velocity monitoring, adaptive optics imaging, and near-infrared spectroscopy. In this paper, we examine high-resolution K band infrared spectra of fifty stars hosting gas giant planets on short-period orbits. We use spectral fitting to search for blended lines due to the presence of cool stellar companions in the spectra of our target stars, where we are sensitive to companions with temperatures between 3500-5000 K and projected separations less than 100 AU in most systems. We identify eight systems with candidate low-mass companions, including one companion that was independently detected in our AO imaging survey. For systems with radial velocity accelerations, a spectroscopic non-detection rules out scenarios involving a stellar companion in a high inclination orbit. We use these data to place an upper limit on the stellar binary fraction at small projected separations, and show that the observed population of candidate companions is consistent with that of field stars and also with the population of wide-separation companions detected in our previous AO survey. We find no evidence that spectroscopic stellar companions are preferentially located in systems with short-period gas giant planets on eccentric and/or misaligned orbits.