In the rubber hand illusion tactile stimulation seen on a rubber hand, that is synchronous with tactile stimulation felt on the hidden real hand, can lead to an illusion of ownership over the rubber hand. This illusion has been shown to produce a temperature decrease in the hidden hand, suggesting that such illusory ownership produces disownership of the real hand. Here we apply immersive virtual reality (VR) to experimentally investigate this with respect to sensitivity to temperature change. Forty participants experienced immersion in a VR with a virtual body (VB) seen from a first person perspective. For half the participants the VB was consistent in posture and movement with their own body, and in the other half there was inconsistency. Temperature sensitivity on the palm of the hand was measured before and during the virtual experience. The results show that temperature sensitivity decreased in the consistent compared to the inconsistent condition. Moreover, the change in sensitivity was significantly correlated with the subjective illusion of virtual arm ownership but modulated by the illusion of ownership over the full virtual body. This suggests that a full body ownership illusion results in a unification of the virtual and real bodies into one overall entity - with proprioception and tactile sensations on the real body integrated with the visual presence of the virtual body. The results are interpreted in the framework of a"body matrix" recently introduced into the literature.