Can spent hit die give a character hit points beyond their maximum?

In D&D 5e can hit die spent during a short rest increase a character’s hit points beyond their maximum number of hit points, thus giving then temporary hit points?

Example: Jed the 2d level the Fighter was wounded, and is at 11 HP. His HP Max is 12 + 8 = 20. (Constitution of 14). The party takes a short rest. Jed rolls a 10 and adds his concentration bonus to get a 12 result. 11+12 = 23.
Would Jed now have (effectively) 23 HP (20 + 3 Temp HP)