Take the cover off the front of the tstat and blow out the Tstat with PC can of compressed air to clean it and the sensor. Also, it also depends on where the tstat is mounted in the RV and if you have any AC air blowing in its proximity. Doug
PS. Is this a recent problem? It was working fine before? If so, then the cleaning of the tstat will probably fix it
Last, without knowing which model tstat you have, it may be just as simple as the 20 year old tstat is worn out(slider assbly and contacs) and needs replaced