Is it the ultra-basic little round one?

Their thermometers are often way off. For a given setpoint, the temp at
which the mercury switch actually makes is highly dependent on how you
mount the stat on the wall- turn it a few degrees and all bets are off.

I'd suggest monitoring the actual temp with an accurate thermometer-
couple bucks for various types at most plumbing/hvac suppliers. Maybe
Radio Shack? Then see if the stat's behavior is consistent, and vary
its set point to match what you want, as accurately measured.

Is your stat locked or something, that you might not be able to change
setting? Extra sweater is much less wasteful than burning oil,
besides. :')
J