In the past years, large particle-physics experiments have shown that muon rate variations detected in underground laboratories are sensitive to regional, middle-atmosphere temperature variations. Potential applications include tracking short-term atmosphere dynamics, such as Sudden Stratospheric Warmings. In this work we use a portable muon detector conceived for muon tomography for geophysical applications, that is, imaging geological objects by quantifying the screening effect they have on the natural flux of cosmic muons. We study seasonal and short-term variations in the moun rate measured in the Mont Terri underground rock laboratory. This site is located in the Jura Mountains in north-western Switzerland, at a depth of ~300 meters below the Earth's surface. We found that the sensitivity to middle-atmosphere dynamics is not only limited to large-scale particle detectors, which are specifically built for neutrino and high-energy particle experiments under high-opacity conditions. Analyzing a year of continuous muon measurements, we found that changes in the thermal state of the atmosphere represent the largest cause of muon rate variations. Furthermore, muon rate variations are also sensitive to the abnormal atmosphere heating in January-February 2017, associated to a Sudden Stratospheric Warming. The estimates of the effective temperature coefficient for our particular case agree with theoretical models and with those calculated from large neutrino experiments under comparable conditions. Finally, we discuss the implications of our observations both for Atmospheric Sciences and for the Geophysics community, the latter aiming to characterize density variations in the subsurface with muon data.