Can the cat converter make my engine run hot?

Hello,

If there is a restriction in the converter it can make the converter overheat and also possibly the exhaust manifold, but it should not overheat the engine. You might have excess heat under the hood, which can possibly make the run hotter than it should.
Keep in mind that when there is restriction in the exhaust it can crate hot spots in the converter or the manifold.

You can use a heat gun to test the temperature the converter and the manifold is exerting. If there is a blockage in the converter there will be substantial temperature difference between the front and the back of the converter.

https://www.2carpros.com/articles/how-to-test-a-catalytic-converter

Keep in mind that the engine can also overheat if you have a restriction in the cooling system. Flushing the system can improve the performance.

https://www.2carpros.com/articles/coolant-flush-and-refill-all-cars

Please let me know of any questions.
Thank you.