Irreversible normal zones leading to quench is an important aspect of high-temperature superconductors (HTS) in all practical applications. As a consequence of quench, transport current gets diverted to the matrix stabilizer material of the high-$T_{c}$ composite and causes Joule heating till the original conditions are restored. The nature of growth of the resistive zone in the superconductor greatly influences the temperature evolution of the quenched zone. In this investigation, a complete mathematical analysis of the temperature profile evolution following a quench in a HTS has been carried out. Such prediction in temperature profile would aid the design of HTS tape-based practical applications in limiting the thermal stress-induced damages in off-normal scenarios.