Gamma-ray spectra from the decay of the giant dipole resonance (GDR) built on excited states of $^{92}\mathrm{Mo}$ and $^{100}\mathrm{Mo}$ nuclei at average spins (9--24)\ensuremath{\Elzxh} and temperatures of 1.35--1.50 MeV were measured, and the parameters of a two-component GDR strength function were extracted. Deformations determined from the fitted component energies are substantially larger than predicted by the rotating liquid drop model, suggesting large thermal shape fluctuations. Widths of the GDR in $^{92}\mathrm{Mo}$ increase from 7.6\ifmmode\pm\else\textpm\fi{}0.1 to 8.6\ifmmode\pm\else\textpm\fi{}0.2 MeV in the spin range of (9--19.5)\ensuremath{\Elzxh} and temperature range of 1.35--1.45 MeV, as compared with the ground-state GDR width of 5.4\ifmmode\pm\else\textpm\fi{}0.2 MeV. In $^{100}\mathrm{Mo}$ the GDR width is nearly constant and equals 9.8\ifmmode\pm\else\textpm\fi{}0.2, 9.9\ifmmode\pm\else\textpm\fi{}0.2, and 10.1\ifmmode\pm\else\textpm\fi{}0.2 MeV at average spins 9\ensuremath{\Elzxh}, 19.5\ensuremath{\Elzxh}, and 24\ensuremath{\Elzxh} and temperatures 1.35, 1.45, and 1.50 MeV, respectively, as compared with the ground-state width of 7.9\ifmmode\pm\else\textpm\fi{}0.2 MeV. The observed difference in the GDR widths between the two molybdenum isotopes at the same temperatures and spins indicates that shell effects are still present at the temperatures studied.