Marinette hated cold days, it was in her blood to feel warm, especially when since she lived in a bakery.
On a cold day she was most likely to stay in her bed than going to school and see Adrien's handsome face, that's to tell you how much she hated the cold.
Now normally she'd just phone Nathaniel (they became friends after that akuma mumbo-jumboa and she'd politely declined his confession) and have him take her to school while using him as a snuggle buddy but unfortunately for her, him and his parents were out of town for a week.
She'd considered calling Alya but she was asleep at this time (because she lived next to the school she didn't bother to wake up early) and the girl developed a mean streak when she didn't get her beauty sleep.
So she decided to just deal with it and go alone, but it was pretty dangerous since she could fall asleep at any moment, that's why she normally went with someone to make sure she wouldn't fall asleep on the road.
She hadn't counted on meeting Adrien on the way, she also hadn't expected a hand to land on her cheek, it wasn't her fault her head leaned to rub against his palm, his hand was just so warm. Her eyes were so heavy and it wouldn't hurt to just rest them a bit, for like two seconds.
Adrien was just walking to school (after he'd ran away from his driver) when he spotted Marinette.
Since she looked a bit dazed he decided to check up on her, it wouldn't do for her to trip and hurt herself. So since they were friend (they were friends weren't they?) he decided to keep her safe, because that's just what friends do.
As he approached her, he called her name several times, seeing that she didn't respond he gently gave her a pat on the cheek to wake her up. He hadn't expected her to start rubbing against his palm while muttering gibberish and then falling asleep against his hand, just like that, in the middle of the road.
Now not knowing what to do he looked around trying to find a solution and then looked at the time only to see that they had only about 15 minutes to get to school.
He finally decided to improvise and give her a piggyback ride to school, which was surprisingly easy since she didn't weigh a thing.
As Adrien entered his class, it was to see the shocked faces of his classmates, he sent a look to Nino that immediately understood and went to sit next to Alya, he installed her on Nino's chair and created a pillow for her with his scarf and laid her head on it while gently brushing the hair of her face.
When Marinette opened her eyes it was to warmth, lights and the gaping faces of her classmates.
She didn't think much of it until she realized that most of the stares were sent her way.
Now that she thought about it how had she even got to school?
The last thing she remembered was seeing Adrien and everything else was just a foggy mess in her head, oh well, the future Marinette could take care of the situation. The nice warmth she felt oozing from the person next the her was enough to convince her to get back to sleep.
She didn't know that she'd later wake up to catcalls, a winking Alya, Nino sending smirks her way and a blushing Adrien trying to explain the situation. She didn't know all that for now she was warm and that was all that mattered.