<p>This paper takes the unsteady natural convection equations as the research object, innovatively incorporates the “Zero-Energy-Contribution” (ZEC) method, and considers the first-order Backward-Euler (BE) and second-order Crank-Nicolson (CN) fully discrete formats based on a low-order nonconforming mixed finite element method (MFEM). It concentrates on the rigorous theoretical analysis and numerical verification of these schemes, with particular dedication to realizing superconvergence behavior. In terms of numerical approximation, for the velocity and temperature fields, the constrained nonconforming rotated <i>Q</i>₁ <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((CNRQ_1)\)</EquationSource> </InlineEquation> element is adopted. For the pressure field, the piecewise constant (<i>Q</i>₀) element is utilized, which attains compatibility with the element of the velocity field and fulfills the inf-sup condition. By applying simple and effective interpolation post-processing approaches as well as flexible techniques, the superclose and superconvergence error estimates of the above fully discrete ZEC-BE and ZEC-CN formats are successfully proved. To verify the correctness and reliability of the important achievements of the theoretical analysis, several numerical experiments are designed carefully, which numerically justify the efficacy and superiority of the proposed MFEMs.</p>