Praise be to Allah.
The evidence for that is the hadith of `Aishah (may Allah be pleased with her), that the Prophet (peace and blessings of Allah be upon him), when he wanted to eat or sleep at the time when he was junub (in a state of impurity following intercourse ), he would do wudu. (Narrated by Muslim, al-Hayd, 461)
Shaykh Ibn ‘Uthaymin said in al-Sharh al-Mumti’: “It seems to me that the one who is junub should not sleep without doing wudu , this is mustahabb, as is also the case with regard to eating and drinking. Some of the scholars said: it is not makruh for him to eat or drink without doing wudu when he is junub.” (Al-Sharh Al-Mumti’, 1/310-311)
And Allah knows best.