Why do some foods have to be cooked only when the pan is really hot

This question is a little vague, but probably your temperature probe is lying to you, or you're not accounting for resting your meat. I would suggest a legit thermometer rather than one that gives you hints about the meat -- you'll have more control over the final product.

Temperature Guide:

• Medium Rare Beef has an internal temp of 145F / 60 Celsius
• Medium Beef has an internal temp of 160F / 70 Celsius
• Well Done (ruined) has a temp of 170F / 75 Celsius

Remember that on resting your beef will rise roughly 10F / 12C in the middle as the heat distributes. So, if you pull the beef out at 160F / 70C, it will be well done by the time you eat it.

If you want Medium Rare, pull it out at 135F / 55C.

Well, you're definitely right. Onions cooked at a high temperature act differently than ones cooked at a low temperature, per "the bible" aka On Food and Cooking. However, it doesn't go in to much of an explanation as to why. Probably the most relevant aspects of what is in there are:

When onions and their relatives are heated, the various sulfur compounds react with each other and with other substances to produce a range of characteristic flavor molecules. The cooking method, temperature and medium strongly affect the flavor balance. Baking, drying, and microwaving tend to generate trisulfides, the characteristic notes of overcooked cabbage. Cooking at high temperatures in fat produces more volatiles and a stronger flavor than do other techniques. (p.311)

Since a low temperature produces less volatiles, I assume that the natural sugars of the onion shine through instead.

It's probably also important to understand where the oniony flavor comes from. The spice, as you describe it, is the onions natural defense mechanism. However, it doesn't exist defacto in the onion, but is rather the result of a chemical reaction. The onion stores very reactive sulfur in the cell fluid, and a seperate trigger mechanism in a storage vacuole. When you cut / crush / cook/ peel the onion, you break the vacuole and the enzyme and sulfur cause a chemical reaction giving off the spice. (p272 & 310)