Using the spin probe predeuterated-2,2,6,6-tetramethyl-4-piperidone-N-oxide (PD-Tempone) at mole fractions about 10(-5) the transition temperatures of ’pure’ 4-cyano-4’-n-pentylbiphenyl (5CB) and four dilute solutions of 3,3-diethylpentane (Et(4)C) at mole fractions between 0.02 and 0.08 in 5CB were determined. This fast approach relies on the smaller coupling constant obtained for the spin probe in the orientationaly ordered nematic phase relative to the isotropic phase. Using an especially designed sample holder in conjunction with a temperature control and monitoring system the temperatures of our samples were controlled to within +/- 0.02 degrees C. The results were used to obtain the phase diagram for the 5CB-Et(4)C system in the concentration range studied.