Metal-organic frameworks (MOFs) are a highly porous crystalline material with potential in various applications including on-board vehicle hydrogen storage for fuel cell vehicles. The thermal conductivity of MOFs is an important parameter in the design and ultimate performance of an on-board hydrogen storage system. However, in-situ thermal conductivity measurements have not been previously reported. The present study reports room temperature thermal conductivity and thermal diffusivity measurements performed on neat MOF-5 cylindrical compacts (ρ = 0.4 g/mL) as a function of pressure (0.27–90 bar) and gas type (hydrogen and helium). The transient plane source technique was used to measure both the non-directional thermal properties (isotropic method) and the directional thermal properties (anisotropic method). High pressure measurements were made using our in-house built low-temperature, high pressure thermal conductivity sample cell. The intrinsic thermal properties of neat MOF-5 measured under vacuum were—Isotropic: k isotropic = 0.1319 W/m K, α isotropic = 0.4165 mm 2 /s; Anisotropic: k axial = 0.1477 W/m K, k radial = 0.1218 W/m K, α axial = 0.5096 mm 2 /s, and α radial = 0.4232 mm 2 /s. The apparent thermal properties of neat MOF-5 increased with increasing hydrogen and helium pressure, with the largest increase occurring in the narrow pressure range of 0–10 bar and then monotonically asymptoting with increasing pressures up to around 90 bar. On average, a greater than two-fold enhancement in the apparent thermal properties was observed with neat MOF-5 in the presence of helium and hydrogen compared to the intrinsic values of neat MOF-5 measured under vacuum. The apparent thermal properties of neat MOF-5 measured with hydrogen were higher than those measured with helium, which were directly related to the gas-specific thermal properties of helium and hydrogen. Neat MOF-5 exhibited a small degree of anisotropy under all conditions measured with thermal conductivities and diffusivities in the axial direction being higher than those in the radial direction. The low temperature specific heat capacities of neat MOF-5 were also measured and reported for the temperature range of 93–313 K (−180–40 °C).