Maybe not... [It looks like Damian needs more than just a towel or cloak at this point, and Izuku tells him as much.]

It looks like you need a place to warm up, though. You're shivering. [However hard Damian might be trying to hide that, Izuku's really sharp-eyed when he wants to be.]

Besides....you just came out of the well, right? [With an outfit like that, Izuku knows he would've remembered seeing him before.] If you warm up at my place, I can answer any questions you have.