How to determine perfect pan temperature for steak?
I don't think there is any single answer to this question, because it would depend on:


The type and thickness of the steak
The starting temperature of the steak
How well you like it done (because the goal is to get enough browning and crust development on the outside, without crossing over into burning, while still cooking the steak through)
The peculiarities of your own equipment, including both your element and your pan (a thick heat retaining pan will have less temperature drop than a thin one, and so require less ongoing source of heat)


Even if we could give you a single answer, it would probably be in terms of the surface temperature of the pan before you put a steak into it, and unless you have an infrared thermometer (which have only become reasonably available in the last 10 years or so, and are not typical kitchen equipment), that answer would not be actionable to you.

So we fall back on less precise methods, saying things like the oil should just be smoking, or that it should be shimmering, or that a bread cube should brown in about 5 seconds. 

Perhaps the best test also requires the most experience to apply.  Hold your hand, open, palm down, over the surface of the pan about 1 inch (2.5 cm) from the surface for a few seconds.  The length of time it takes for it to become uncomfortable tells you hot how the pan is.   It should be about 3-4 seconds, but again, requires experience to use this method, and everyone's perception varies.

In any case, you are going to have to employ trial and error as you learn the idiosncracies of your own burner, and your own taste in steak.

That said, there are a couple of methods that are more forgiving.  Possibly the best is cooking sous-vide, and only searing for browning afterwards in the pan, but not everyone has the equipment and wherewithal of that method.

A technique that anyone can do is to put the steak in a slow oven (about 250 F 120 C) until it is cooked through about 5 degrees F (2-3 C) below the doneness you like, as tested with an instant read thermometer.  IT will be wan and pale looking but this is okay.  You then sear it in a quite hot pan, until it is brown and delicious.  This should only take a couple of minutes, since the steak is cooked through; you are just developing the crust.  This shorter time should be much less likely to burn.



Note:  within limits, a thicker steak requires a lower temperature, but this is very limited.

Thick steaks truly require a two-stage cooking method, such as the ones outlined above, or traditional pan roasting (searing in the frying pan, then transferring to the oven).

In the end, though you will always have to come back to experience with your equipment, and your preferences on how you do your steaks.