This paper presents a mathematical model on the longitudinal mid-span extension of the Tamar Bridge, UK by using 6 months data of temperatures and an extension starting from July 2010. Linear models of temperature input-extension output were identified for all the combinations of input temperatures. The model using two temperatures, one temperature on the top of the mid-span section and the other on the bottom, was found to be the best with the fitness value 95.9% while single-temperature input models had maximum fitness 80%. This observation might be explained by the temperature gradient at the section: in the existence of the temperature gradient, two temperatures in the section may represent the temperature distribution of the section well while a single temperature can't. A further study needs to be carried out to verify it by a thermal simulation on a Finite Element model of the bridge.