As a novel class of magnetic materials, altermagnets (AMs) exhibit properties such as zero stray field and strong spin-split bands. These properties give AMs advantages over ferromagnets and antiferromagnets in forming heterostructures with superconductors. In Josephson junctions composed of AMs, the current-phase relations (CPRs) display a 0-π transition by tuning parameters such as the barrier potential and the length of AMs. The altermagnetic Josephson junctions have broad application prospects in fields such as quantum device research and quantum computing. In this study we investigate the temperature dependence of CPRs in a two-dimensional superconductor/altermagnet/superconductor Josephson junction, where we choose the d_xy symmetry in the AM. Based on the Bogoliubov-de Gennes (BdG) equation and the Furusaki-Tsukada formula, we calculate the CPRs in a large scope of temperature region. We find that in addition to 0-π transitions, the junction can also develop other types of transitions including π-0, 0-φ , φ-0, φ-π ones by varying the temperature from 0 to superconducting transition temperature. As the type of CPRs changes, we find that a turning point can appear, leading to either non-monotonic behavior or an abrupt change in the second derivative of the temperature dependence of critical current. We regard that this temperature dependence of the CPRs originates from two key mechanisms: decaying pairing potential and the growing occupation of high-energy Andreev bound states with increasing temperature, where both the current magnitude in individual transport channels and the relative weight of different channels change simultaneously. This study provides a method of tuning the properties of altermagnetic Josephson junctions via temperature, offering potential support for experimental exploration of such junctions and the development of future superconducting spintronic devices.