We investigated temperature behavior of superconducting fault current limiters (SFCLs) during quenches. Knowledge on temperature behavior during quenches is important to the design of SFCLs, because the temperature of SFCLs is related to their stability. SFCLs were fabricated by patterning $Au/YBa_2Cu_3O_7$ thin films grown on sapphire substrates into meander lines by photolithography. A gold film grown on the back side of the substrate was patterned into a meander line, and used as a temperature sensor. The front meander line was subjected to simulated AC fault currents, and the back line to DC current. They were immersed in liquid nitrogen during the experiment for effective cooling. Overall, temperature at the back side of SFCLs was close to that at the front side. It was closer at the beginning of faults, and at lower applied voltages. Temperature distribution at the back side was even except at the edge, as at the front side. These results tell that the whole SFCL was heated to similar degree during quenches, and that effective cooling of SFCLs at the back side is as important to the stability of SFCLs as at the front side. The results could be explained with the concept of heat transfer within the film.