There is a need to develop tools for mastitis management in goats and to measure the effects of milking machines on teats. Infrared thermography (IRT), as shown in cows, was a good candidate for early mastitis detection and focusing on milking equipment and settings implicated in potential problems. The aim of this study was to test IRT to detect udder inflammation and the effects of mechanical milking on teats in relation to inflammation status, udder balance, and teat shape in Alpine goats. IRT spectra were compared before and after milking in 551 goats from three commercial herds compared to their individual SCC (somatic cell count). We found no regression or trend between logSCC and IRT measurement or response to milking, even in highly inflamed goat udders. The effect of milking was significant (p < 0.05) with global temperature reduction after milking, but differences were seen between teat parts and unbalanced half udders. The highest reduction in skin temperature was observed at the teat orifice (−1.06 ± 0.05) and the lowest at the teat barrel (−0.37 ± 0.05). The teats with long barrels showed more IRT reactions, which clearly indicates poor adaptation to the liners used. In conclusion, the IRT was not able to detect mastitis, but it is a good tool to diagnose the effects of the milking machine in order to adapt milking equipment and settings to the goats and improve their welfare.