Themsen was brought up in FC Nordsjælland before moving to FC Helsingør as an U15 player in the summer of 2020. Ahead of the 2023–24 season, 17-year-old Themsen moved to Randers FC, where he became part of the club's U-19 squad.[2]
On 23 February 2024 Themsen was on the bench for Randers in the Danish Superliga for the first time.[3] However, he had to wait until 7 April 2024 to make his debut as Themsen was substituted for his first Danish Superliga match, coming off the bench to replace Noah Shamoun against Hvidovre IF.[4][5]
On 3 June 2024 Randers confirmed that Themsen had signed a new three-year contract, so the agreement now expired at the end of June 2027.[6] On 19 December, his contract was extended again, this time keeping him at the club until 2028.[7]