Astronomical seeing parameters calculated based on the Kolmogorov turbulence model cannot fully evaluate the effect of the natural convection (NC) above a solar telescope mirror on the image quality, as the convective air motions and temperature variations of the NC are significantly different from the Kolmogorov turbulence. In this work, a new method based on the transient behaviors and frequency characteristics of NC-related wavefront error (WFE) are investigated in detail and used to evaluate the image quality degradation caused by a heated telescope mirror, aiming to make up for the deficiency of astronomical seeing parameters with the conventional method in evaluating the image quality degradation. Transient computational fluid dynamics (CFD) simulations and WFE calculations based on discrete sampling and ray segmentation are performed to quantitatively evaluate the transient behaviors of the NC-related WFE. It clearly exhibits apparent oscillatory characteristics, which are coupled by main oscillation with low frequencies and minor oscillation with high frequencies. Moreover, the generation mechanisms of two types of oscillations are studied. The conspicuous oscillation frequencies of the main oscillation caused by heated telescope mirrors with varying dimensions are primarily lower than 1 Hz, suggesting that active optics may be adopted to correct the main oscillation of NC-related WFE while the adaptive optics may correct the minor oscillation. Furthermore, a mathematical relationship between WFE, temperature rise, and mirror diameter is derived, revealing a significant correlation between WFE and mirror diameter. Our work suggests the transient NC-related WFE should be considered as one of the critical supplements to the mirror seeing evaluation. © 2023 Optica Publishing Group.