Control of temperature variation is of primordial importance in particular areas of biomedicine. In this context, medical treatments such as hyperthermia and cryotherapy, but also the development and use of hydrogel-based biomaterials are of particular concern. To enable accurate temperature measurement without perturbing or even destroying the biological tissue or material to be monitored, contactless thermometry methods are preferred. Among these, the most suitable are based on magnetic resonance imaging and spectroscopy (MRI, MRS). Here, we address the latest developments in this field as well as their current and anticipated practical applications. We highlight recent progress aimed at rendering MR thermometry faster and more reproducible, versatile and sophisticated, and provide our perspective on how these new techniques broaden the range of applications in medical treatments and biomaterial development by enabling insight into finer details of thermal behavior. Thus, these methods facilitate optimization of clinical and industrial heating and cooling protocols.