  Utilizing the highly correlated quantum NOON states of particles, we have
implemented a proof-of-principle quantum thermometer using the NMR technique
for measuring the variation of local magnetic field with the temperature
variation. The system used was the star-topology system of hexafluorophosphate
molecules and the thermometer showed a sensitivity of $85nT/ ^o C$. Using the
hexafluorophosphate and the trimethylphosphite spin systems, we have quantified
the advantage of the quantum protocol over the classical one for measuring
magnetic field. The quantum protocol showed the best performance for a time
evolution in the quantum circuit of $T = 20ms$, where the errors in the
measurement scaled as the Heisenberg limit $1/N$.
