Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.