In this work, we study the pairing Hamiltonian with four particles at finite temperatures on a quantum simulator and a superconducting quantum computer. The excited states are obtained by the variational quantum deflation. The error-mitigation methods are applied to improve the noisy results. The simulation of thermal excitation states is performed using the same variational circuit as at zero temperature. The results from quantum computing become close to exact solutions at high temperatures, and demonstrate a smooth superfluid-normal phase transition as a function of temperatures as expected in finite systems.