Fluid inclusions in stalagmites are becoming increasingly important for paleoclimate research. Within this framework, noble gas thermometry, based on noble gases dissolved in water from fluid inclusions, provides quantitative estimations of cave air paleotemperature. Two major issues of Noble Gas Temperature (NGT) determination on speleothems are (1) the potential lack of enough water for the analysis and (2) the presence of trapped gas not dissolved in water that can be released during the analysis from biphasic or all-gas fluid inclusions, as its contribution to the bulk noble gas signal can hinder NGT results. Although the step-crushing method helps to reduce the second issue, it also decreases the amount of water available for the calculations. In order to obtain reliable NGT results with low uncertainties, a major challenge is still to reach a balance between sufficient water for analysis and a small amount of “atmospheric” gas. The difficulty is that the extraction process cannot be standardized since it strongly depends on the type of sample. The objective of this work is to investigate how the characteristics of the speleothem can determine the adequacy of the extraction process. For this purpose, we consider a stalagmite from a Mediterranean cave that consists of columnar elongated calcite and contains a significant quantity of fluid inclusions, which suggests good potential for NGT analysis. Results, however, were poorly satisfactory. Trying to understand the source of the problems, an integrated study of petrography and petrophysical features was performed. The samples were found to be different depending on the stage of coalescence of crystals and thus separated into “open” and “closed” fabrics. Classic petrographic analysis and non-destructive (nuclear magnetic resonance) techniques were used to characterize the type and amount of fluid inclusions present in both types of fabrics. The study indicates that the closed fabric (total coalescence of calcite crystals) has most water trapped in water-filled, small intracrystalline fluid inclusions that usually contain very little gas. This fabric is very suitable for NGT determination, but since the amount of water is quite small, the sample should be crushed in only one step with a large number of beats to break all the inclusions. In contrast, samples with open fabric (partial coalescence of calcite crystals) contain a higher amount of water and, also, gas-filled large intercrystalline fluid inclusions. For this fabric, step-crushing of the sample is necessary. However, the low amount of water left for the second and third crushings could lead to flawed NGT results. Thus, we suggest modifying the method to get rid of part of the gas in the first crushing while leaving enough water for the following steps. This work shows the importance of characterizing speleothems and fluid inclusions, including their petrography and petrophysical characteristics, before starting NGT analysis, allowing the selection of the most favorable samples and the customization of the step-crushing procedure.