Exclusive measurements of high-energy γ rays have been performed in ¹²⁴Ba and ¹³⁶Ba at the same excitation energy (∼49 MeV) to study the properties of the giant dipole resonance (GDR) over a wide N/Z range. The high-energy γ rays are measured in coincidence with the multiplicity of low-energy γ rays to disentangle the effect of temperature (T ) and angular momentum (J ). The GDR parameters are extracted employing a simulated Monte Carlo statistical model analysis. The observed γ-ray spectra of ¹²⁴Ba can be explained with prolate deformation, whereas a single-component Lorentzian function which corresponds to a spherical shape could explain the γ -ray spectra of ¹³⁶Ba. The observed GDR width in ¹³⁶Ba is narrower compared to that of ¹²⁴Ba. The statistical model best-fit GDR cross sections are found to be in reasonable agreement with the thermal shape fluctuation model (TSFM) calculations. Further, it is shown that the variation of GDR width with T is well reproduced by the TSFM calculations over the temperature range of 1.1–1.7 MeV.