We report on the rotational diffusion dynamics of Rhodamine 640 (R640) in the series of normal aliphatic alcohols methanol through n-decanol. By performing these measurements for excitation of both the S-1 and S-2 excited singlet states, we are able to determine unambiguously that R640 reorients as a prolate rotor in these solvents, that the first excited singlet state of R640 is long-axis polarized and that the second excited singlet state of this probe molecule is short-axis polarized. Our reorientation data indicate close association of the solute with several solvent molecules. Treatment of the data using Chuang and Eisenthal's formulation reveals that the measured component of the rotational diffusion constant is the same for excitation of either the S-1 or S-2 excited states, but for several of the solvents studied, we find the reorientation times for S-1 excitation to be slower than those for S-2 excitation. We understand this phenomenon in the context of transient heating caused by the excess energy deposited into the R640 molecule when the S-2 state is excited. These data reveal a transient temperature change in solution on the order of 10 K, with the temperature gradient existing over the first solvent shell surrounding the probe molecule.