In this paper, an extensive experimental program was performed to define the effects of elevated temperatures on the tensile properties of GFRP and BFRP rebars, with different matrix compositions and surface preparations. Two different test setups were used: steady-state and transient temperature conditions. The steady-state test was performed over the temperature range of 70–290 °C, and the transient temperature test was conducted at a load level of 15–80% of its tensile strength before being subjected to elevated temperatures. Combining these tests allowed for the examination of specimens subjected to a wide range of temperature and stress levels. The obtained experimental results are presented, including a comparison of the rebars with different types of fibres and matrices. The experimental program included more than 70 specimens in total. Moreover, the test methodology is discussed in detail, and recommendations addressing the standardization of these test setups are made. Furthermore, the main objective of the paper is to present temperature-dependent strength curves for different types of FRP rebars, providing necessary information for a less conservative but safe design of concrete structures reinforced by FRP and subjected to fire.