<p>This paper presents a one-dimensional Bresse system with thermoelasticity of type III and constant delay. The objective is to investigate and establish the asymptotic behavior of vibrations in a circular arch problem coupled with damping due to the thermal effect subject to constant delay feedback. By applying the semigroup method, we prove that the system is well-posed. Furthermore, with some assumptions on the delay feedback and wave speeds of propagation, we prove that the dissipation through this thermal effect is solely sufficient to counteract the time delay effect and the vibrations in the displacements, thus causing exponential and polynomial energy decay of the system’s solution. Our stability results are achieved by employing the multiplier technique, which mainly involves constructing an appropriate Lyapunov functional equivalent to the system’s energy.</p>