REYKJAVIK, Iceland — As the coach of the most successful national soccer team in Icelandic history, Heimir Hallgrimsson has had to make some sacrifices. This year, for instance, he was abroad with the team and could not dress up as his favorite mythological character, Gryla the child-snatching troll, at the Christmas party in Heimaey, his hometown.

Because Gryla’s costume obscures the wearer’s identity, few people realized that Hallgrimsson was for many years the man in the troll suit. “I don’t know who did it this year,” his nephew, Arne Olafsson, said, “but he was not as aggressive as Heimir.”

Coaching a team bound for the World Cup has also left less time for Hallgrimsson’s original job, looking after people’s teeth in his dental practice in Heimaey (population 4,300), a 5.2-square-mile volcanic island off Iceland’s south coast.

“It’s a good way to relax,” Hallgrimsson said this year during a lull in Iceland’s soccer schedule here. Despite high winds and a looming snow and ice storm, he was heading home for some delayed dental therapy (for himself). “Some coaches play golf, shoot reindeer, whatever — everybody has something,” he said. “But I really enjoy going back home to my clients.”