This Cochrane Review by Saxena et al from 2014 reveals a paucity of RCTs to support moderate therapeutic  hypothermia in TBI patients. It remains a widely used modality in spite of this absence of evidence.

“In order to further explore the preliminary findings provided by animal models and observational clinical studies that suggests there may be a beneficial effect of modest cooling for TBI, randomised trials designed to explore the effect of these interventions on patient-centred outcomes are needed”