High-transport critical-current density Jc is essential for major bulk applications of the high-Tc superconductors. The critical temperature Tc of the 2212 Ag sheathed tapes was found to increase by quenching the samples, but the transport critical-current density Jc for a slow-cooled sample was higher at low temperature. Jc as well as its temperature dependence was found to be influenced by the heat treatments, i.e., whether the sample was quenched or slow cooled after the sintering heat treatment. The zero-field Jc was found to be quadratic in 1-T/Tc for the slow-cooled sample, while a linear dependence was observed for the quenched sample. These results are explained in terms of the weak-link structure.