Does Glycerol give silver mirror test with Tollen's Reagent?
Your guess of formation of Acrolein is a pretty good one, as indicated in this answer, but a boiling water bath will probably not give you the 160°C temperature you are looking for to convert glycerol to acrolein

This question is most similar to yours and has a pretty good answer by bon. The answer says:


  However, from personal experience, gentle heating of a primary alcohol with Tollens' will cause a small amount of oxidation and result in a fine black precipitate.


It is most likely that Glycerol is undergoing a small amount of oxidation to any of it's oxidation products (most probably glyceraldehyde, since that gives tollen's test) and this oxidized compound is giving a positive tollen's test.