Time-resolved single-photon counting has been used to measure the decay of fluorescence anisotropy of a number of aromatic hydrocarbons in methylcyclohexane excited by synchrotron radiation. Changing the temperature (-60 to -140 degrees C) produces large changes in the viscosity, eta. Most solutes were excited both parallel and perpendicular to the emission axis with the aim of determining all three principal rotational diffusion coefficients, D. The results are compared to predictions from hydrodynamic theory made using the "slip" and "stick" approximations and literature data for the n-alkanes and other solvents. Rotation times should be proportional to eta/T, i.e., D eta/T should be constant. This is found to be approximately true for 9,10-disubstituted anthracenes; it does not hold for anthracene, perylene, and triphenylene for which D eta/T increases markedly on cooling. Also, against prediction, the ratios between D values for different molecular axes are found to change with temperature.