It is well known that the electrical impedance of biological tissues is very sensitive to their temperature. In this paper, we have analyzed the effects of temperature change on the phase of magnetic resonance images obtained with external current injection. It has been found that the local phase in the current injected magnetic resonance image can be changed noticeably when local temperature change appears at a part of the tissue. At the experiments with a 0.3 Tesla MRI system, we observed the local phase changes at the phantom images when the phantom temperature was varied between 25 -45$^{circ}C$. We think that the current injection MRI technique can be used for in-vivo monitoring of the temperature inside biiological tissues if the relation between the local temperature and phase can be quantified.