Thordarson has won seven of 11 league matches in charge of Crewe
Crewe manager Gudjon Thordarson will continue with his rolling contract and remain as manager of the Alex after receiving clarification over his job.
The 53-year-old wanted assurances over certain aspects of the club before committing himself to Crewe.
He told BBC Radio Stoke: "I'm very happy with my work and I'm enjoying it, but you never know what can happen.
"It's down to other people to decide my future. All I care about now is getting the right results."
Thordarson has been a revelation since arriving at the Alexandra Stadium on 24 December.
He has won seven of the 11 league games he has taken charge of Crewe, and in the process taken them out of the relegation zone in League One.
He has not pleased everyone with his management style, however, and Thordarson has responded angrily to critical comments from midfielder Michael O'Connor.
The Northern Ireland international was sent on loan to Lincoln after a breach of discipline.
"It doesn't hurt me at all," said Thordarson. "It's sad to see a young lad not looking to himself and seeing how he can improve.
"I'm not bothered about him any more, he can do what he likes, but he is still our player and as our player he has to be aware of what he says and what he does."
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