[Sherlock can tell how tired he is by how sluggish his evaluation of the clerk at the hotel is. Wife, but currently not a harmonious matrimony given the faint lines on his face suggesting his current bed is the sofa. One cat. Or perhaps two? He's far too tired to tell, and definitely too tired to care.

He merely follows John into the bedroom and sinks onto the nearest bed, laying fully clothed on top of the mattress without even bothering to take off his coat and shoes.]

I came here to sleep, John, nothing else. Use the shower if you wish, but be quick about it, you will require more rest than me and so it's imperative that you get into bed as soon as possible.