Color centers in diamond and nanodiamonds can be utilized as quantum sensors for measuring various physical parameters, particularly magnetic and electric fields, as well as temperature. Due to its small size and possible surface functionalization, fluorescent nanodiamonds are attractive systems for biological and medical applications since they can be used for intracellular experiments. This review focuses on fluorescent nanodiamonds for thermometry with nanoscale spatial resolution for living systems. The current state of the art, possible further development, and potential limitations will be discussed here.