Yes it does this. The thermostat is part of a control-loop with feedback. The phenomenon you notice has a name. It's called 'hysteresis' and you can read all about it here-> http://en.wikipedia.org/wiki/Hysteresis.
For a thermostat, the hysteresis is designed-in -- to avoid uncontrolled rapid switching that could happen if the system switched on and off at exactly the same temperature.
(It's not due to latent heat convection stugod unless you mean something similar but I don't recognise the terms you used.)