ot a propellor-on-a-shaft type stirrer, you can stir the contents of your D ewar flask easily enough, but most places I've been rely on Teflon coated m agnets spun by an external magnetic field, and those are hard to get spinni ng in a Dewar flask.
beaker lasts for quite a while.
My probe is 'open to the elements', in direct contact with the water.
George H.