Transient sensitivity analysis aims to obtain the gradients of objective functions (circuit performance) with respect to design or variation parameters in a simulator, which can be widely used in yield analysis and circuit optimization, among others. However, the traditional method has a computational complexity of $O\mathsf{}\mathrm{(}{N}^{\mathrm{2}}\mathrm{)}$ for objective functions containing circuit states at $N$ time points. The computational complexity is too expensive for large $N$, especially in time-frequency transform. This paper proposes a many-time-point sensitivity method to reduce the computational complexity to $O\mathsf{}\mathrm{(}N\mathrm{)}$ in multiparameter many-time-point cases. The paper demonstrates a derivation process that improves efficiency by weighting the transfer chain and multiplexing the backpropagation process. We also proposed an early-stop method to improve efficiency further under the premise of ensuring accuracy. The algorithm enables sensitivity calculation of performances involving thousands of time points, such as signal-to-noise and distortion ratio and total harmonic distortion, with significant speed improvements.