In this work we study electromagnetic properties of a resonator recently suggested for the search of axions-a hypothetical candidate to explain dark matter. A wire medium loaded resonator (called a plasma haloscope when used to search for dark matter) consists of a box filled with a dense array of parallel wires electrically connected to top and bottom walls. We show that the homogenization model of a wire medium works for this resonator without mesoscopic corrections, and that the resonator quality factor Q at the frequency of our interest drops versus the growth of the resonator volume V until it is dominated by resistive losses in the wires. We find that even at room temperature metals like copper can give quality factors in the thousands-an order of magnitude higher than originally assumed. Our theoretical results for both loaded and unloaded resonator quality factors were confirmed by building an experimental prototype. We discuss ways to further improve wire medium loaded resonators.