This study evaluated different strategies to increase gas−liquid mass transfer in a randomly packed gas stirred tank reactor (GSTR) continuously fed with second cheese whey (SCW), at thermophilic condition (55 °C), for the purpose of carrying out in situ biogas upgrading. Two different H2 addition rates (1.18 and 1.47 LH2 LR−1 d−1) and three different biogas recirculation rates (118, 176 and 235 L LR−1 d−1) were applied. The higher recirculation rate showed the best upgrading performance; H2 utilization efficiency averaged 88%, and the CH4 concentration in biogas increased from 49.3% during conventional anaerobic digestion to 75%, with a methane evolution rate of 0.37 LCH4 LR−1 d−1. The microbial community samples were collected at the end of each experimental phase, as well as one of the thermophilic sludge used as inoculum; metanogenomic analysis was performed using Illumina-based 16S sequencing. The whole microbial community composition was kept quite stable throughout the conventional anaerobic digestion (AD) and during the H2 addition experimental phases (UP1, UP2, UP3, UP4). On the contrary, the methanogens community was deeply modified by the addition of H2 to the GSTR. Methanogens of the Methanoculleus genus progressively increased in UP1 (47%) and UP2 (51%) until they became dominant in UP3 (94%) and UP4 (77%). At the same time, members of Methanotermobacter genus decreased to 19%, 23%, 3% and 10% in UP1, UP2, UP3 and UP4, respectively. In addition, members of the Methanosarcina genus decreased during the hydrogen addition phases.