Thiim began in karting before winning the 2006 Danish Formula Ford Championship. In 2007 he transitioned to touring cars, finishing fifth in the Seat León Supercopa Germany and contesting the Danish Touring Car Championship in a BMW 3 Series. He won the 2008 Seat León Supercopa Germany outright, taking eight victories from 16 races, then moved to the Porsche Carrera Cup Germany in 2009 and finished fifth while also claiming the SP3T class win at the 24 Hours of Nürburgring in a works Volkswagen Scirocco.
Thiim continued in Porsche machinery through 2013. He finished fourth in the 2011 Porsche Carrera Cup Germany with a win and four podiums, then raced in both the Porsche Supercup and Porsche Carrera Cup Germany in 2012, finishing third in each. He also collected three ADAC GT Masters podiums in a Porsche 911 that year. In 2013 he became Porsche Supercup champion and secured the overall victory at the 24 Hours of Nürburgring.
Thiim joined Aston Martin Racing as a full-time factory driver for the 2014 FIA World Endurance Championship season, following a three-race stint as a replacement for Allan Simonsen in 2013 after the Danish driver's fatal accident at Le Mans. His move to the GTE Pro class with Aston Martin proved a long and successful partnership. Thiim claimed the FIA WEC GT Championship in 2016 and repeated the feat in the 2019–20 extended season, giving him two world titles in the GT category.
In 2024 Thiim added a major endurance win when he took overall victory at the 24 Hours of Spa.
Thiim subsequently competed in the Deutsche Tourenwagen Masters and the GT World Challenge Europe Endurance Cup for Comtoyou Racing, broadening his career beyond the WEC platform that had defined his peak years.
Alongside his professional career, Thiim built a substantial presence in the sim racing world through iRacing. He streams races regularly on Twitch and YouTube, where he has accumulated over 20,000 subscribers, referring to his following as "TeamThiim." He also organised a charity 12-hour sim racing event to raise funds for Danish children with cancer, attracting more than 45 teams and 200 drivers and raising over 100,000 DKK.
Thiim represents a rare generation of professional racing drivers who simultaneously competed at the highest level of real-world endurance racing while maintaining active and engaged sim racing careers. His two WEC GT titles with Aston Martin, his 2013 Porsche Supercup championship, and his 2024 Spa victory across a career built on consistency and mechanical empathy mark him as one of Denmark's most accomplished GT drivers.