Thornton, who shared the first-round lead at Alwoodley with new county champion Sam Rook, of Lindrick, added a two-over-par 73 to his opening 71.
It gave the former England Boys' Order of Merit winner a one-shot advantage over Rook, who carded a 74.
Two shots back of Thornton after a 72 is Leeds Golf Centre's Ben Firth, while Carris Trophy holder Barclay Brown (Hallamshire) moved into contention with a level-par 71and is tied sixth on 147.
Skipton's Max Berrisford, recent winner of the Yorkshire match play championship, dipped seven shots lower than his opening 81 with a 74 to make the cut and progress to today's final two rounds.
"I played just steady; nothing amazing, nothing awful," said halfway leader Thornton. "But that's all you need round there. All to play for (on Thursday)."
The North of England championship, won last year by David Hague, the England international from Malton & Norton, is the last event on England Golf's men's Order of Merit.
Yorkshire have three players sitting inside the top 10 – Hallamshire's Alex Fitzpatrick, Brabazon Trophy holder Nick Poppleton (Wath) and Lindrick's England international Bailey Gill – but none are playing at Alwoodley.
Fitzpatrick is in America where he has begun a golf scholarship at Wake Forest, in North Carolina, alma mater of the legendary Arnold Palmer.
Alwoodley, which next year will stage the English amateur stroke play championship, the Brabazon Trophy, welcome visitors and will be offering an autumn green fee rate of Â£55 in November and December. For more information contact the club on 0113 268 1680 or email [email protected]