We performed temperature dependent photoluminescence measurements of exciton states in GaAs laterally coupled quantum dots. The temperature dependence of the radiative decay time was used to investigate the density of states to study the intra-relaxation of thermally excited exciton states. We analyzed the density of states in laterally coupled quantum dots by observing the radiative decay time of exciton states as a function of temperature, where the decay time of exciton photoluminescence was calibrated with respect to photoluminescence intensity to extract the radiative decay time. In the case of laterally coupled quantum dots, a one-dimensional structure can be formed by elongation along the direction of coupling between two quantum dots. However, this assumption is not valid when the size in the uncoupled direction is comparable to that in the coupled direction. From experimental measurements, the power order of the temperature dependence was found to be 0.8, which corresponds to a quasi-one-dimensional system (similar to T-alpha=0.8), which is in between a two-dimensional (alpha = 1) and a one-dimensional (alpha = 0.5) density of states. This is due to several factors including a large size along the uncoupled direction, an extended wave function owing to optical coupling, and the presence of dark states.