MRI is a unique tool for minimally invasive thermal ablation in that it can provide both targeting, monitoring and control during the procedure. Monitoring is achieved by using MRI temperature mapping. In this review the relevant physics is explained as a background to the state-of-the-art methods for computing temperature maps as well as the more cutting edge methods. The review covers both methods to monitor heating and cooling of tissue and explains temperature mapping using Proton Resonance Frequency shift, T1 mapping, diffusion mapping, R2* mapping and thermal models.