  We study the backscattered current in a Luttinger liquid in the presence of a
point like 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 $\tau_{R}$ as
function of the electron-electron interaction and the temperature, such that
for $\tau_{R} < 1$ ($> 1$) 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.
