Thornton, who shares the lead on nine under par with and Turin native Francesco Molinari and Chile’s Felipe Aguilar, shot six birdies and dropped just a single shot, at the par four 17th.
Higgins has just one top-three finish to his credit in more than 200 European Tour events but feels the course suits his game.
The world number 684 said: “I didn’t hit it as close as yesterday but if you keep hitting the fairways on this course you can manage it and get a lot of opportunities and I am good at doing that.”
Molinari, who carded a second round of 67, has been the centre of attention all week as he bids to claim his national open for the second time, but said: “It adds a little bit of pressure but it’s good, it gives you an extra motivation to do well.”
Ryder Cup team-mate Nicolas Colsaerts had looked set to at least maintain his overnight share of the lead but bogeyed the 16th and 18th – where he duffed a chip – to return a 71 to lie eight under alongside Higgins and England’s Steve Webster.