Cullen asks the Inquisitor to share his bed long before they actually have sex.
He misses the feeling of another body in bed next to him. When he was a boy, he and Branson used to share a bed, and when it would storm out, his sisters would pile in too. Once he left for Templar training, it took him months to get used to sleeping alone–that was probably when his trouble with sleeping started, in truth. He missed the feeling of a warm body next to him, the comfort of knowing on a very basic level that he was’t alone, no matter how dark the night or frightening his dreams.
And when she agrees, cuddles in close to him and nuzzles against his chest in the darkness, well, she feels like home.