We fabricated a prototype for SiC trench MOSFET with intergrated trench Junction Barrier Schottky Diode (TJBS) to realize low reverse on-state voltage drop (V_{R_on}) and low switching power loss under different temperatures. A TJBS is integrated at the sidewall of a trench nearby the gate trench to inactivate the PN body diode, which not only reduces V_{R_on}, but also eliminates the conductance modulation effect during the free-wheeling state. Thus, the reverse recovery charge will not increase with the increase of temperature, which ensures that the reverse recovery loss for the free-wheeling diode and turning-on loss (E_on) for the nearby MOSFET almost remain unchanged under high temperature operation. The fabricated SiC trench MOSFET with cell pitch of 8 um shows a R_on,sp of 5.95 mΩ·cm² and V_{R_on} of 2.6 V at 300 A/cm². Further TCAD optimization based on the measured data shows that a low R_on,sp of 2.52 mΩ·cm² and V_{R_on} of 2.04 V can be obtained when shrinking the cell pitch to 5 um. Compared with a simulated CoolSiC^TM MOSFET, the proposed SiC trench MOSFET shows that E_on and turning-off loss (E_off) at 25 °C are reduced by 32.8% and 80.7%, respectively. The total power loss is reduced by 54.5% to 61.8% when temperature increases from 25 °C to 175 °C.