How accurate is the hand technique for grilling?

While I suspect that the formula is mostly reliable if you repeat the experiment with the same person, I found the individual heat sensitivity varies a lot. Most professional cooks and seasoned homemakers can handle (pun intended) higher heat than those who rarely expose their hands to high temperatures. In our home, we’ve had heated discussions about whether the dishes in the just finished dishwasher are too hot to touch or not. And this is just one example.

If you exclude the differences between individuals, using your own hand’s heat sensitivity to gauge a temperature range is absolutely possible (as long as a few degrees don’t matter). It takes time and practice - which is usually described as “experience”. I personally don’t think in “degrees” though, but more in categories like “too cold” / “should be ok” / “too hot” and a few steps in between.

So in short, if you need a precise temperature, get a thermometer. If you are still working on judging by hand, either get a thermometer or plan a few trial-and-error loops. And sometimes the exact temperature is not important for a recipe to work.

Using the X-time at Y-distance formula may work, if your heat sensitivity is similar to the author’s.

I'll answer by way of similar situations:

• I have an italian coffee machine with an external milk frother. This works by shooting hot air into the milk. You hold the milk in a very thin-walled metal jug and heat it until you feel the correct temperature. This works quite explosively and fast. The hand method works incredibly well here; I've not seen a thermometer yet which would be fast enough.
• I roast coffee beans. While many go with digital temperature sensors etc., and in a professional setting you absolutely want to do that to get reproducable (and sellable) results, I went the route of going by visuals, sound and especially smell. This is of course very much "analog" and non-scientific, but over time my experience tells me pretty well what's going on. Including when parameters (like outside temperature, bean type/age, charge volume and so on) change.

For cooking, I use the "hand test" for e.g. judging when to put the eggs into the pan, or for grilling, to get a picture of if the coal is "ready", or too hot, or too cold.

In all of these cases, the "hand technique" is accurate enough. I've not measured anything to see how close I get, but it fulfills its purpose of giving good results. I could never tell you exact measurements (X inches for Y seconds), all these tests are meant to be individual for your situation.

I hear that some people are able to decide when a steak is rare/medium/well done by pressing on it; but for these things I'd prefer an internal thermometer. I'm pretty sure that if I had lots of experience grilling steaks (which I don't), over time some "thumb test" would maybe work as well.

I wouldn't say that the technique is accurate at all. However, it is reliable, if the measuring instrument (you) is well "calibrated" (trained).

There are lots of good cooks which go by intuition. After years of cooking, they have gotten a very finely tuned sense of how to do things. Their brain does what is best at - it takes all information available to it (memories, heat perception, smell, sense of passing time, etc.), does some unconscious pattern recognition, and arrives at the decision "the grill is at the right temperature now", which turns out to be correct. This is how they get consistently good results almost every time.

Cooks who do not have that kind of experience can try finding other means to get consistently good results. Measuring the temperature with a thermometer is a good one, since it is usually the most important factor in baking and roasting. They replace the decision based on intuition with one based on a technical measurement.

Advice like the one you discovered is well-meant, but misleading. When an experienced cook tries to teach you how to do it "their way", they try to put in words whatever they think is going on in their head. They know they use their hand to check if the temperature is good enough, so they try to tell you how they came to the conclusion, e.g. "if you feel a burning feeling in the skin after 3 seconds, it's all right". There are two problems with that approach. First, as Stephie said, the connection between external stimulus (heat) and its interpretation by your CNS that turns it into a thought ("I have a burning feeling in the skin") is very individual. Second, it is not correct that the decision ("now is the time to put on the food") is made based on just that one stimulus. The cook cannot tell you how they made it, since it is an unconscious process. They are second guessing themselves.

So, if you are not yet an expert-with-great-intuition cook, then using this method will not result in consistently well baked food. At that stage, if you want that, you should be using a thermometer.

There is nevertheless a reason why you might want to use the method. If you want to turn into an expert cook with great intuition, the way to do it is by training your intuition through multiple repetitions. Your learning progress is determined by a combination of the number of repetitions, and the attention/concentration you use in each repetition. So, if you take some moments to pay attention to how the heat feels on your hand when roasting your food, you will become an expert sooner than if you ignore the feeling. Still, if the quality of the food is important to you, you should rely on the thermometer and not the feeling until you have trained your intuition a lot.

The measurement is not accurate for glass blowers. Might also be true for others who work with extremely high heat (people in foundries and such).

But for your average home chef, it gives a close enough estimation of the temperature that you can reduce the chance of burning / severely undercooking your food. But I'd only recommend it if it's for something that you're watching closely and can pull off / move to a cooler area of the grill if it's cooking too quickly, or add additional time as needed.

I wouldn't recommend this for dishes which must be cooked to a specific temperature (eg, sugar glazes, cheesecake, many egg dishes), or cook unsupervised without an opportunity to adjust (eg, soufflé)