I used to do driveability on Honda automobiles, back when much of what came in the shop was carbureted. Much of my diagnoses were for lean running @ idle & cruise. This was my 'bread and butter'.

We put a fitting in the end of a garden hose, that took a small ball valve and a couple feet of quarter inch hose off the end of it.

When opened, you could get a nice stream about the diameter of a number 2 pencil. This would find intake leaks that wouldn't show up with other methods, such as brake clean, or propane. Or that high $$$ Snap-On smoke generator (mostly smoked the boss' wallet...).

Pinpointing the area of the leak was really important on these cars, because they would have 100 vacuum fitting joints (literally) under the hood.

If there was a leak, other methods might find it, but water would.

Edit: in the original post... The car runs hot at idle. IME, heat can be caused by timing, and can also be caused by lean mixture (and also by a mechanical considerations...). I suspect Dwayne's question about where the idle mixture screws end up to make the car run is probably right on the mark.

In my world, people very rarely made adjustments to their cars, they just took them to the shop when they didn't run right. So, if they had an air leak, it would usually show up by feeding propane into the intake air 2 offset the lean condition.

But, if the idle mixture has been adjusted to compensate, that test would not necessarily do anything.

FWIW, I would try putting water over that intake before removing it. It's a far cheaper and easier test to run then removing the manifold, taking it to the machine shop, putting it back on... And if there's anything I like better than something cheap, it's something easy.