@anotherone
Doggo guy wants to sit in the kotatsu but is a tsundere and doesn't want to outright admit it so he's coughing and the princess thinks he has a cold
Not sure I get the end there, about 'the price', is she now cold because she got used to being warm? Someone else explained about the doggo but that doesn't explain the princess's attitude.
@marcyvq It's a Japanese superstition that you'll catch a cold if you sleep in a kotatsu. Since the princess did that, she now has a cold, and she is misunderstanding that the cold is some sort of price that must be paid for using a magical device.