No strong team needs relief pitching more than the Detroit Tigers. No reliever is hotter than Jesse Crain. Don’t be shocked if Crain is closing games against the White Sox when the teams meet in Detroit before the All-Star break. When general manager Rick Hahn decides it’s time to cut his losses on the 2013 season, he’s going to make his inventory of players available to 29 teams, including the four in the American League Central. He told me so early Tuesday, and then reiterated those views to reporters covering the Sox in Minneapolis. Crain is capturing a lot of attention with a first half that Joe Mauer says is worthy of a spot on the AL All-Star team. He’s in the last season of the three-year deal he received after seven years with the Twins, and pitching coaches Don Cooper, Bobby Thigpen and Juan Nieves have helped him become a better pitcher than he was when he arrived. There’s no evidence the Tigers are pursuing Crain — and colleague Mark Gonzales reported the Rangers and Dodgers had scouts watching Crain in Houston last weekend — but he’s a perfect fit for a bullpen that has Jose Valverde (9-for-12 in save chances, five homers allowed in 18 1/3 innings) as the closer and could be without Octavio Dotel all season because of a mysteriously sore elbow. The reflex rumor making the rounds has Tigers GM Dave Dombrowski waiting to see if the Phillies will trade Jonathan Papelbon. But Seattle-based analyst Dave Cameron suggested the other day at that the new-and-improved version of Crain makes more sense than Papelbon. Their stuff has become comparable with the evolution of Crain’s secondary pitches, including a curveball that he has been using to help get ahead of left-handed hitters. The one unknown is whether Crain can handle the heat as a closer. He has four saves in 527 career outings and, earlier in his career, had a tendency to give up costly home runs in big spots. But he hasn’t allowed a homer in his last 44 outings, since Sept. 1, and always has said he wanted the challenge to close games.