Temperature range for seasoning a carbon steel pan

In the restaurant, we just poured some coarse salt into the pan and put it on high heat (gas range). Then tossed the salt around and poured out the results.

At home, with the electric range top, I put my carbon steel wok on a burner on high (it's scary, but it works) and watch as everything burns off and the carbon steel "steel" look returns.

The brilliance doesn't last but the surface does. I use a cotton rag that is very lightly dabbed in peanut oil to brush the surface while it's hot.

And then it darkens when it's cooling/cooled.

Don't hesitate to go hot, really hot. Just be safe at the same time.

It looks like your pan needs a hard cleaning and a re-seasoning. I run into this about once every 2-3 months (depending on how much I use it).

My tried and true method is to break some rules at this quarterly cleaning. I'll scrub with an abrasive scotch-brite, SOS Pads or similar scrubbing pad. During this time I often use about a quarter cub of baking soda, and towards the end I'll even use a little bit of dawn dish soap to make sure I've removed all of the particles, which amount to fine iron filings.

I've even resorted to very high grit sand paper to even out some areas in very serious issues on my handle. Now it's important to rinse and dry the pan COMPLETELY.

I then carefully rub crisco (less smokey than lard) all over EVERY surface of the now shiny and smooth pan.

Then, invert pan in oven over a baking sheet or foil to catch any mess, and bake the pan at 500F for roughly an hour or two, or until it is uniformly black.

If you have access to a clean, wood burning put, that's what my grandmother swore by, but I find the 500F oven more consistent.

I am not certain if this would work for your high carbon steel pan pictured in the first photo though. I would read up on that.