The UV absorption spectra of neat water clusters (H2O)(n) of sizes in the range of n = 8-50 are computed. The simple model used for the excited states includes the dependence of the excitonic interactions on both the intermolecular and intramolecular coordinates. For a cluster (H2O)(n), n excitonic potential energy surfaces are computed for geometries in the Franck-Condon region. The Coker-Watts potential is used to describe the interactions in the electronic ground state, and molecular dynamics simulations are performed to sample geometries for the classical Franck-Condon calculations. There are numerous crossings of different excitonic potential surfaces for (H2O)(n) in the range of the geometries sampled. The main findings are (i) the main absorption peak of (H2O)(n) shifts to the blue and increases in width as the cluster size n is increased; (ii) the widths of the absorption bands increase with temperature, e.g., for (H2O)(20), the width is 1.2 eV at 80 K and 1.6 eV at 220 K; (iii) several well-resolved peaks within the absorption band are found for some of the systems at certain temperatures, and in such cases, each of the peaks generally results from absorption into different excitonic states; (iv) although the absorption peaks are strongly shifted to the blue, with respect to the (H2O) monomer, for some cluster sizes, a weak absorption tail to the red side is also observed as the temperature increases.