Interpreting measurement data from continuous monitoring of civil structures for structural health monitoring (SHM) is a challenging task. This task is even more difficult when measurement data are influenced by environmental variations, such as temperature, wind and humidity. This paper investigates for the first time the performance of two model-free data interpretation methods: Moving Principal Component Analysis (MPCA) and Robust Regression Analysis (RRA) for monitoring civil structures that are influenced by temperature. The performance of the two methods is evaluated through two criteria: (1) damage detectability and (2) time to detection with respect to two factors: sensor-damage location and traffic loading intensity. Furthermore, the performance is studied in situations with and without filtering seasonal temperature variations through the use of a moving average filter. The study demonstrates that MPCA has higher damage detectability than RRA. RRA, on the other hand, detects damages faster than MPCA. Filtering seasonal temperature variations may reduce the time to detection of MPCA while the benefits are modest for RRA. MPCA and RRA should be considered as complementary methods for continuous monitoring of civil structures.