Born in Växjö, Wirdheim began racing karts at age ten, until the age of fifteen, winning the Southern Swedish Karting Championship. In 1996, he progressed to single-seaters in Swedish Formula Ford 1600 Junior Championship where he took the championship title in 1997 with a staggering 17 wins. In 1998 and 1999 he raced in the Formula Palmer Audi Championship, but they were two disappointing seasons with only two visits to the podium in total.
In 2000, he switched to the German Formula Three Championship. Then, during 2001 in addition to winning at Nürburgring and A1-Ring, he took three pole positions including one at Macau Grand Prix. For the season of 2002 Wirdheim switched, this time to International Formula 3000, joining Arden International. He finished fourth overall, in addition to being named Rookie of the Year, and helping Arden to win the team title in the championship.
Wirdheim stayed with Arden in the following season of 2003 that would prove successful both for the team and driver. He dominated the championship so much that an obligatory pit stop for tire change was introduced at the end of the season in an attempt to level the advantage, but Arden managed to do better pit-stops overall than other teams and still came out on top. Wirdheim became the first Swede to win the championship in its 19-year history, breaking Justin Wilson's previous record of most points won in one season of the series. However, at Monaco, when driving to an easy win on the streets of Monte Carlo, Wirdheim slowed down to wave at his pit-crew believing he already had taken the checkered flag and was overtaken by Nicolas Kiesa, metres away from the actual finish line.
At the end of 2003, Wirdheim had been noticed by several Formula One team bosses, giving him opportunity to test with both Jordan and BAR. After turning down an offer to drive Champ Car, Wirdheim signed with Jaguar as third driver performing the Friday testing for the team at Formula One Grand Prix weekends during the 2004 season.
For the 2005 season, Wirdheim turned to the Champ Car World Series to join the HVM racing team. Run by former Pacific F1 team boss Keith Wiggins, the team was underfunded after losing its previous Herdez backing, and a lack of testing made it difficult for the team to be competitive. After mediocre results, Wirdheim and the team decided to part ways after 11 races into the season.