The thermal contact conductance was measured for eight pairs of metal specimens in a vacuum environment: three stainless steel (304) pairs, three aluminum (606I-T6) pairs, and two aluminum-stainless steel pairs. The dissimilar material pairs were tested more than once. Four experiments were conducted at cryogenic temperatures (mean interface temperature from 110 K to 131 K), six were conducted at room temperature, and three were conducted above room temperature. Each specimen in a pair possessed approximately the same surface texture. The conductance was measured as a function of contact pressure from approximately 2 MPa to 9 MPa. A modified Greenwood and Williamson elastic contact model was used to correlate the obtained data. The experimental results for stainless steel pairs showed good agreement with the elastic model, whereas the aluminum and aluminum-stainless steel pairs did not. Experiments with dissimilar material pairs were conducted to evaluate the repeatability of the experimental procedure and to analyze whether or not a thermal rectification effect was observable. In both cases, the experimental procedure was found to be repeatable, and thermal rectification was not observed.