  To achieve quantum computing using semiconductor spin qubits, the spin qubits
must be precisely controlled. However, unexpected noise limits this precision
and prevents the implementation of error correction codes. Specifically,
frequency shifts have been found to suppress one-qubit gate fidelity. Although
the exact source of the frequency shifts remains unclear, several experiments
have indicated a relationship between the frequency shift and heating from the
control signal. Based on these results, we modeled the heating effect using the
low-temperature dependence of specific heat from the Debye model to simulate
qubit control with frequency shifts. This model quantitatively reproduces some
of the experimental results and makes it possible to simulate qubit gates with
temperature-dependent frequency shifts. The simulated control fidelity of the
proposed model was consistent with the experimental results, demonstrating that
a gate fidelity above $99.9$% can be achieved in a hot environment.
Additionally, our comparison of the two temperature-dependent frequency shift
models reveals the condition for a microscopic frequency shift model in which
the variance of the frequency shift is limited to a specific range.
Furthermore, we investigated gate fidelity using the DRAG method and
demonstrated the utility of temperature-dependent simulations.
