The copper transport (COPT/Ctr) family plays an important role in maintaining metal homeostasis in organisms, and many species rely on Ctrs to achieve transmembrane transport via copper (Cu) uptake. At present, the Ctr family is widely studied in plants. However, there are few reports on the use of Ctrs in edible mushrooms. In this study, the Pleurotus ostreatus CCMSSC00389 strain was used as the research object, and the addition of exogenous copper ions (Cu2+) increased the temperature tolerance of mycelia, maintained the integrity of cell membranes, and increased mycelial density. In addition, four PoCtr genes were further identified and subjected to bioinformatics analysis. Further research revealed that there were differences in the expression patterns of the PoCtr genes under different temperature stresses. In addition, the biological function of PoCtr4 was further explored by constructing transformed strains. The results showed that OE-PoCtr4 enhanced the tolerance of mycelia to heat stress and H2O2. After applying heat stress (40 °C), OE-PoCtr4 promoted the recovery of mycelia. Under mild stress (32 °C), OE-PoCtr4 promoted mycelial growth, maintained cell membrane integrity, and reduced the degree of cell membrane damage caused by heat stress. It is speculated that OE-PoCtr4 may maintain the integrity of the cell membrane and enhance the heat resistance of mycelia by regulating the homeostasis of Cu2+.