Temperature distribution and the deformation behavior under temperature are important parameters in the design and evaluation of concrete pavements. In this paper, in order to study the horizontal distribution of the temperature effect on rubberized concrete pavement (RCP), the distribution differences of temperature, temperature gradient and strain at different horizontal locations were analyzed based on fiber Bragg grating test technology. The relationships between temperature and strain and between temperature gradient and strain were also investigated. The results show that within a cycle of temperature or temperature gradient change, the time of temperature increase or temperature gradient increase is only 1/4 of the whole cycle, significantly less than the time of the temperature or temperature gradient decrease. Comparing the center, edges and corner of the pavement, the horizontal distribution of temperature and temperature gradients in the RCP is uneven, and the greatest negative temperature gradient is experienced at the corner of the pavement, which is 25 °C·m−1 greater than the temperature gradient at the center. The negative temperature gradient at the corner of the concrete pavement exacerbates the bottom deformation at the center and edge of the pavement, especially in the X-axis direction at the center and in the Y-axis and Z-axis directions at the edge. The relationships between temperature and horizontal strain at the center and edge of the RCP have a significant hysteresis effect and are markedly stronger than those at the corner. Moreover, when the temperature gradient is less than −23.4 °C·m−1 or greater than 14.5 °C·m−1, the curling effect at the edge of the RCP is more obvious.