Temperature & time necessary to carbonize all organics
There's a lot of exciting, and not well defined, chemistry that happens with seasoning cast-iron cookware.  Essentially, you are creating a cross-linked polymer film that is hydrophobic, providing a "stick-free" surface.  There are many many websites claiming the "best way" to season (or re-season) cast-iron cookware.  Few of these sites (and I'll let the OP and visitors search for those on their own) are based on science.  (Although I am not going to question tried and true family secrets, passed down from generation to generation.)  One site in particular makes a fairly convincing argument for seasoning that is science-based.  I suggest this approach can help restore your pot.

I suspect what has happened is that the scrubbing did remove the seasoning and exposed base metal to water and oxidation - your pot rusted.  The "soapy contaminants" is probably iron oxide rather than something from the dishwater, although there are such products as metal soaps which are metals chelated to long-chain fatty acids.

As for heating the pot to burn off all the residue - I doubt this is the most effective use of your time.  Scrubbing with acidified water to remove the iron oxide and a long seasoning session with an easily cross-linkable oil should get your pot back to (or better than) original condition.