We study the backscattered current in a Luttinger liquid in the presence of a pointlike weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter τ_R as a function of the electron-electron interaction and the temperature, such that for τ_R <1(>1) the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter K through time measurements in transport experiments at fixed voltage.Facultad de Ciencias Exactas