  Nanoscale thermometry is paramount to study primary processes of heat
transfer in solids and is a subject of hot debate in cell biology. Here we
report ultrafast temperature sensing using all-optical thermometry exploiting
synthetic nanodiamonds with silicon-vacancy (SiV) centres embedded at a high
concentration. Using multi-parametric analysis of photoluminescence (PL) of
these centres, we have achieved an intrinsic noise floor of about 10 mK
Hz$^{-1/2}$, which is a thousand-fold increase in the readout speed in
comparison to the current record values demonstrated with all-optical methods
of comparable spatial-resolution and precision. Our thermometers are smaller
than 250-nm across but can detect a 0.4$^\circ$C change of temperature in a
measurement taking only 0.001 second. The exceptional sensitivity and
simplicity of these thermometers enable a wide range of applications such as
temperature monitoring and mapping within intracellular regions and in
state-of-the-art solid-state electronic nanodevices.
