Sentence 1: Dan shivered because he was cold. 
 Sentence 3: Dan looked at the time and saw how late it was 
 Sentence 4:  Instead of starting a fire he put on more layers of clothes 
 Sentence 5:  Dan was warm enough to last until bed time 
 Option 1: He'd gotten so engrossed in work he hadn't started a fire. 
 Option 2: He decided to get a fire going in the fireplace.