Can I get an accurate temperature reading from a flask with a built-in thermometer well?
The thermal conductivity of air isn't very high, when compared to organic solvents or silicon oils used for heating baths. Consequently, one doesn't place thermometers in the vapour phase above the liquid when monitoring or controlling temperatures. (That is, of course, except for distillations, where you want to measure exactly that - the temperature of the vapour phase in the head.)

In your case, it might help to fill the well with the same silicon oil that you use for the heating bath. In order to keep the rod thermometer in place (rather than letting it float), you might want to use a Quickfit adapter (similar to this one) that fits the joint of the well.