<p>This study investigated the impact of chirped laser profiles on self-focusing and second harmonic efficiency (SHE) during propagation in a pre-formed plasma channel with an exponential density ramp in the quantum regime. Using the W-K-B and paraxial ray approximations, we derived expressions for self-focusing and the SHE for Sinh-Gaussian, Tanh-Gaussian, and Gaussian profiles. The results indicated that the Sinh-Gaussian profile achieved shorter distances and deeper focusing compared to the Gaussian profile, while the Tanh-Gaussian profile surpassed both in focusing ability. The maximum SHE, which relies on initial laser self-focusing, is most incredible for the Tanh-Gaussian and Sinh-Gaussian profiles when compared to the Gaussian. We observed self-focusing and SHE enhancement for positive chirped pulses, and the opposite effect on negative chirped pulses. The relativistic ponderomotive force in thermal quantum plasma also enhances the SHE compared to the cold quantum regime and relativistic plasmas. The Sinh-Gaussian profile provides better SHE at both near and far propagation distances. In contrast, the Tanh-Gaussian profile, although similar to the Gaussian, exhibits significantly improved self-focusing and the SHE at intermediate distances within the plasma.</p>