Engine Room Checks underway

Depends what size boat your talking about. On a 140 a crew of 5 running 24/7 we did hourly checks. On the crew boats we'd do it once every 4 hours or so. On the smaller boats I ran we check at the start of the day and at the end. Otherwise we're busy running, but we're checking gauges, exhaust and feel every second. Never used a heat gun unless a problem was suspected.

For underway "generic" checks (as opposed to specific troubleshooting), you might consider a thermal camera rather than an IR heat gun.
They are indeed more expensive, but not anymore as much as they used to be.
And for quickly spotting any possible anomalies, they are in another league compared to IR guns.
Also for all electrical components, btw - panels, breakers, batteries, you name it.

I don't bother with a IR gauge, you'll see any trouble on your normal gauges. Every hour or two, open the hatch and take a look inside.

Well you can't spot a problem with a single faulty injector, for instance.
And in fairness, it ain't easy with an IR gun either, but if you look at the exhaust manifold with a thermal camera, significant temperature differences between each cylinder are (relatively) easy to notice.
Another thing I like to check occasionally is the raw water circuit temp: hull intake, and pipes coming out of the heat exchanger & intercooler.
That can obviously change a lot, depending on the sea water temp, but the DELTA should remain constant, if the HE and CAC are working as they should. And the raw water pump as well.
I've never seen that type of temperature monitored in any dashboard gauges.

Every 30 minutes. Access is a no brainer on our boat. Walk down the stairs open the respective engine room door and do a quick scan for obvious issues and then point and shoot. Yes, IR gun as I don't trust the old mechanical gauges and suspect two of them of being off. Top of the 4 thermostats, and the exhaust just after the shower head. The whole thing takes less time than it took to type this up. (I'm a slow typist...... )

It's a game of "what has changed since last time". Being an observant person is better than knowing everything and having decades of mechanical experience. Is the smell different, vibration different, sound (even with ear protection on) different?
Are the normal leaks larger than usual? How about little pieces of rubber around the belts?
Don't overthink the IR gun. If it's a twin engine boat, whatever you shoot should be about the same on the other side. Shaft logs, exhaust points, water pumps are a good place to start.
As for frequency, every few hours would be good. Might as well write it in the log book.

I don't consider myself expert enough to say what is right. But it's been my observation as a heavy consumer of internet boat forums, blogs, and videos, that scheduled engine room checks done with an IR gun seem to be more common on passagemaking vessels like Nordhavn et al.. where they will check the engine room and take and log IR readings and compare them to prior readings on some schedule. I've seen people claim they do this as frequently as hourly or at every watch change, perhaps 4-6hrs. But this is on passages of 24hrs to multiple days. Regular engine room checks under weigh on boats that expect to be at dock/anchor each night seem much less common. My practice, and I suspect that of most "day" boaters is a check/inspect at the end of the day and fluid checks before shoving off the next day. If it's a long run 5+ hrs then I may pop the engine room hatch and have a quick peek. Otherwise I'm relying on my gauges along with my senses.

Being a real expert and being able to say what is right don't always go hand in hand.
Imho, your practice is absolutely fine, and I fully agree that it's what most day boaters do.
Aside from the not so rare ones who don't do anything at all, that is.

It's also true that the most popular practice in passagemaking vessels is different, more accurate and frequent, but there are two good reasons for that:
First and foremost, a serious failure could be more dangerous when you are hundreds of miles from land and from any possible help.
Second - but also rather relevant - when it takes forever to get nowhere, you might as well spend some of your time in the e/room...

Actually, the most memorable stories in my mind were failures that happened (too) close to land...... "Out there" I have time, and tools.

I see your point, and I don't disagree.
I also noticed that you previously mentioned your habit of 30 minutes checks, which certainly deserves respect.
But if you apply that also while on coastal, daily trips, in my experience you are rather a remarkable exception than the norm.

Probably...... A lifetime of aviation has engrained a pretty solid "keep an eye on things". I will admit that my engine room setup, 4 doors in the hallway, is conducive to sticking your head in there. If I had to move salon furniture I would probably be installing cameras and more sensors.

Yeah those Hat engine rooms are nice. With an owner who loved to drive, and 4 door in the hall I made a lot of checks underway even though we put in each night. Good thing too since one of the things I found was a lot of water when shaft log leaked.

Rule #2..... Keep the water out of the boat.

Engine room checks are hourly at night (because we have two guys at the helm on two hour, staggered shifts, so first thing the guy coming on does is the ER check), and every 2 hours during the day (when we only have one guy at the helm and watch changes every 2 hours).. IR checks only every 8 - 12 hours (but the first is soon after we have settled in at a comfortable cruise speed). The hourly checks are focused on listening, smelling and looking for anything unusual. IR is focused on exhaust manifolds, alternators and turbos. My gensets are not in the engine room, so those never get checked while underway. So far, so good.