Microwave impedance measurements indicate a non-linear absorption anomaly in
single wall carbon nanotubes at low temperatures (below 20 K). We investigate
the nature of the anomaly using a time resolved microwave impedance measurement
technique. It proves that the anomaly has an extremely slow, a few hundred
second long dynamics. This strongly suggests that the anomaly is not caused by
an intrinsic electronic effect and that it is rather due to a slow heat
exchange between the sample and the environment