new manager (who is not officially managing my team)
You need to be clear on your relationship with this temporary manager. I'd probably start with a conversation with your former manager's manager. What is the interim reporting line? Has the temporary manager been asked to keep an eye on any important projects until a permanent manager is found? Once you understand what your manager's manager expects from your team, you'll be better placed to respond to this temporary manager.
Somebody should be managing your team until a permanent manager is found, even if they don't have the time to. This person may be your manager's manager, this new temporary manager or someone else.
[My new manager has asked] "Please summarize your meeting with x and send it to your team"
A manager is responsible for all the work that their team does, and ensuring that the team members are working together well. They can only do this if they understand what the team is working on.
You've agreed to a meeting with x. That means you had something business-relevant to discuss with x. If it's relevant to you, then it is also relevant to your manager. They don't need to know every word that was discussed in the meeting but a summary is relevant. That could be as simple as "I explained bugs BUG-123 and BUG-456 to x. They are going to come back with some suggested fixes." That means we someone else runs into BUG-456 they know it's already being dealt with and can move on.
If the company wants the temporary manager to oversee the project, and you don't want them to be constantly sticking their nose into what you're doing, then you need to make sure that you're pro-actively keeping them informed about your status. That way you get to control when and how the information is shared, and your manager has confidence that the project is on track.
Of the 4-5 apartment sized fires our teams are currently handling, the one that is being overmanaged is a warm summer breeze
This is either an indication that the temporary manager doesn't have a good understanding of your teams' status - in which case, why not? If you think that you shouldn't be switching attention away from the apartment sized fires than you need to highlight those larger fires to your manager.
Or it's an indication that they are paying particularly close attention to a specific project or client. Maybe your company is trying to win a new contract with a client and they want to make sure that the existing projects are running super-smoothly. Maybe it's the only project that your manager's manager has asked the temporary manager to keep an eye on. This comes back to understanding the reporting lines. Ultimately there needs to be one manager ultimately responsible for 100% of your work, so that they can make the tough decision of ignoring one client/project so you've got time to deal with another one.