Get rid ASAP
He is a temp
Go to your manager and get the authority to get a different temp hire plus a guarantee he will not get the full time role.
He is trying to impress your boss and your boss will not be the only person he is playing office politic with.
Remember both your boss and HR signed off on your promotion so he is trying to tell whoever was involved that they did not do their job right when they picked you.
You need to document the conduct via your boss and HR.
He is a bully and undermining your role as well as you personally.
as in if you dont have the technical background to do the job other more senior managers are in the same boat as you.
You are new you dont need to be over spending time on him.
Your basic case to your boss is
He is there to do specific tasks
This is to make both your jobs easier by working within the team, chain of reporting etc.
He has decided to not just do his job.
He has decided to engage in an active campaign of resource mismanagement.
Financial decision is having him is costing extra money. it should just be his salary and a little of yours now its a higher proportion of yours and some of your bosses too.
If your boss wanted a day to day reporting line he would have arranged that.
Your boss promoted you to not have to deal with the BS from the role the new hire carries out. The new hire is creating work for him.
By undermining you with co-workers and his juniors, he increases the risk that some of your team not trusting the reporting lines and systems designed to produce "whatever" and that a preventable error occurs (they need to be able to skip him and whistleblow to you the boss and other senior managers).
For your boss one of the benefits of you is that he should have no direct responsibilty for the new hires output (errors will happen) As an old boss was fond of warning shit rolls down hill (or plausable deniability). The new hire is busy building a documented dam above your bosses head. (when it should be above yours 🤷). You boss will know this too.
You should be able to speak with your boss with regard to the challages you are facing with the new hire. And if necesssary look for some training on people management and HR conflict resolution