To investigate the dependence of giant dipole resonance (GDR) width on temperature (T ) and angular momentum (J ), high energy γ -ray spectra were measured in the reaction ²⁸Si+¹²⁴Sn at E28_Si = 135 MeV. The J information was deduced from multiplicity of low-energy γ rays. The GDR parameters, namely, the centroid energy and width are extracted using statistical model analysis. The observed variation of the GDR width for T ∼ 1.2–1.37 MeV and J ∼ 20h–40h is consistent with the universal scaling given by Kusnezov et al., which is applicable in the liquid-drop regime. The GDR input cross sections extracted from the statistical model best fits are compared with thermal shape fluctuation model (TSFM) calculations and are found to be in good agreement. The TSFM calculations predominantly favor the noncollective oblate shape, while the statistical model fit with both prolate and oblate shapes describes the data. The present data together with earlier measurements indicate a very slow variation of the GDR width for T ∼ 1.2 to 1.5 MeV. The observed trend is well explained by the TSFM calculations, although the calculated values are ∼4%–13% higher than the data.