In the present article, we consider a porous thermoelastic system with distributed delay term in second sound, by using the energy method combined with multiplicative technique, we show the polynomial decay estimate of (1) with (3) in Theorem 2.7 and exponential stability of (1) with conditions (38) in Theorem 3.4. A new restriction on delay term depending on the time in (4) is used to show that the solution energy should be stable. The importance of the present research lies with describing the role of Dirichlet conditions in the nature of stability.