<p>Tempered fractional derivatives extend classical fractional derivatives by adjusting long-term memory effects while preserving the characteristic features of fractional dynamics. This, in turn, enhances both modeling accuracy and computational efficiency. This paper proposes an adaptive tempered Caputo fractional derivative that introduces an order-dependent tempering factor to model fading memory effects more realistically. The proposed derivative preserves the main properties of the classical Caputo derivative and naturally reduces to the integer-order derivative when the order is an integer. We establish analytical properties of the proposed derivative, including its integral representation, corresponding fractional integral, and Laplace transform. In addition, we develop a second-order accurate numerical scheme to approximate the proposed derivative for given functions. We present numerical examples that demonstrate the influence of the tempering parameter. The results confirm that the proposed derivative effectively regulates long-term memory while maintaining the nonlocal nature of fractional dynamics.</p>