The 10-year-old joined the Naas handler last year after a brief retirement early in 2018.
He showed he still retains plenty of ability with an easy success at Cork in August, before respectable efforts to finish fourth to Bedrock and Apple's Jade in graded company.
The 2015 Hatton's Grace winner is set to tackle the larger obstacles now for the first time, and Cullen has been pleased with his schooling ahead of his assignment in the two-mile PMF Beginners Chase.
"He's been schooling well at home and we'll probably start him off there and see how we get on," said Cullen.
"He has jumped plenty of fences. We've had him away to the Curragh and schooled him at home. We'll dip our toe in the water and see how he gets on.
"He's been running well over hurdles, maybe he's not up to Grade One standard over hurdles anymore, but we'd be hoping dropping back to a beginners' chase he should be fairly competitive.
"He probably wants to go a bit further now he's getting a bit older, but it's a case of trying to get suitable ground and they are giving a good cut in it for Thursday.
"If he puts in a clear round we can always step him back up in trip again. We'll see how we get on."
As well as the Hatton's Grace, highlights for Arctic Fire when he was trained by Willie Mullins also included the 2017 County Hurdle at Cheltenham, where he was second to Faugheen in the Champion Hurdle of 2015.
