Memristor is a promising device as a fundamental building block for future unconventional system architectures such as neuromorphic computing, reconfigurable logic, and multibit memories. Therefore, to facilitate circuit design using memristors, accurate and efficient models spanning a wide range of programming voltages and temperatures are required. In the first part of this series, we propose a behavioral model for temperature dependence of nonvolatile switching dynamics of TiO x memristors. We begin by describing pulsed resistance transients (PRTs) of the memristors and then we use a multistage methodology to establish bias and temperature dependence of the model parameters. The proposed model is then shown to accurately describe the PRT characteristics of Pt/TiO x /Au and Pt/TiO x /Pt memristors.