Héðinn competed in the Icelandic Championship in 1991, but did not play in another until 2006, where he finished second. He also did not play in Chess Olympiads during this period, returning in 2008 to score 4/7. In 2009, he won the Reykjavik Open on tie-break over Yuriy Kryvoruchko and Hannes Stefánsson. He played again for Iceland at the 39th Chess Olympiad, scoring 6/10. He has since won the Icelandic Championship twice more: in 2011 and 2015.