Is it permissible for someone who has had intercourse with his wife, then the dawn prayer call (adhan) was made and he could not find hot water for ghusl, to perform ablution (wudu') and pray in congregation for fear of missing the prayer time, and because he did not wish to disturb anyone?

Your friend's action is incorrect for three reasons: He could have taken the water from you, and his claim of fearing to disturb you is not a legitimate excuse. Secondly: The preponderant opinion is that he is obligated to perform ghusl (definition) (ritual bath) even if the prayer time has elapsed. Thirdly: He performed wudu' (ablution) instead of ghusl, and this is invalid. One who is unable to perform ghusl due to a legitimate excuse is obligated to perform tayammum (definition) (dry ablution), not wudu'. He is excused due to his ignorance, and he and his wife are obligated to make up that prayer.