The Dons knew not to underestimate their amateur opponents after requiring a last gasp try to beat them two years ago in the same competition.
First half tries from Ben Johnston and Misi Taulapapa helped the hosts establish a 12-0 half time lead at the Eco-Power Stadium.
Aaron York and Greg Burns added their names to the trysheet to take the game out of the reach of the National Conference League side.
Harry Woollard scored a late consolation try for Thornhill.
The third round draw will take place on Tuesday evening.