<p>The temperature behavior of the topological index <i>C</i>₁ of the chiral superconducting <i>d</i> + <i>id</i> phase of a two-dimensional single-band model on a triangular lattice has been studied. It has been found that the temperature dependence of the topological index fundamentally changes at carrier densities, at which the nodal points of the Brillouin zone approach the Fermi contour of the normal phase. It has been shown that the topological index <i>C</i>₁ in a wide temperature range is close to <i>C</i>₁ = 4 (–2) when the nodal points are located far inside (outside) the Fermi contour. However, when nodal points approach the Fermi contour, these values are maintained only at low temperatures, and values close to <i>C</i>₁ = 1 in a wide temperature range. It has been assumed that such a topological crossover in the system under consideration can lead to significant changes in edge states in a similar open-boundary system.</p>