A sample of 1.53$\times$10$^{9}$ cosmic-ray-induced single muon events has been recorded at 225 meters-water-equivalent using the MINOS Near Detector. The underground muon rate is observed to be highly correlated with the effective atmospheric temperature. The coefficient $\alpha_{T}$, relating the change in the muon rate to the change in the vertical effective temperature, is determined to be 0.428$\pm$0.003(stat.)$\pm$0.059(syst.). An alternative description is provided by the weighted effective temperature, introduced to account for the differences in the temperature profile and muon flux as a function of zenith angle. Using the latter estimation of temperature, the coefficient is determined to be 0.352$\pm$0.003(stat.)$\pm$0.046(syst.).