  The Planck mission will provide full-sky maps of the Cosmic Microwave
Background with unprecedented angular resolution (~ 10') and sensitivity (DT /
T = 10^-6). This requires cryogenically cooled, high sensitivity detectors as
well as an extremely accurate control of systematic errors, which must be kept
at micro-K level. In this work we focus on systematic effects arising from
thermal instabilities in the Low Frequency Instrument operating in the 30-100
GHz range. Our results show that it is of crucial importance to assure "in
hardware" a high degree of stability. In addition, we provide an estimate of
the level at which it is possible to reduce the contamination level in the
observed maps by proper analysis of the Time Ordered Data.
