The MIRS (MMX InfraRed Spectrometer) infrared spectrometer is part of the scientific payload of JAXA's (Japanese Space Agency) Martian Moon eXploration (MMX) mission. From the reflected sunlight by the planetary surfaces, MIRS will provide information on the Mars atmosphere and the mineralogy and chemistry of its moons. Spectra carried out by the instrument (0.9-3.6 $\mu$m) include the thermal emission from the surface, which needs to be modelled and removed to extract the compositional information. In this study, to find an efficient and rapid way to thermally correct infrared data, we developed a simple thermal emission correction based on blackbody fits, and quantify its relative error. To test the method, we generated synthetic spectra of Phobos by using a thermophysical model. We found that the method can produce reflectance spectra with only a few per cent errors, although some undercorrection of the thermal contribution is observed. Compositional information may still be retrieved through the position of absorption bands, despite the thermal emission correction can leave some uncertainties in its strength. We conclude that the method could be used for a first and quick analysis for interpretation of the MIRS data. We also applied our thermal correction methodology to real CRISM (Compact Reconnaissance Imaging Spectrometer for Mars) observations of Phobos. The method looks reliable with a satisfactory removal of the thermal contribution, confirms the presence of an absorption band centred around 2.8 $\mu$m, and reveals an apparent absorption at 3.2 $\mu$m. However, we are not able to confirm the reality of the 3.2 $\mu$m band at this stage, because of the presence of an artefact in CRISM data.