KEYWORDS (HeroClix-Core-Rulebook-v.2017.03-REVISED-8.25.17, page 32)
If a character gains a keyword, it stays for the rest of the game. I am wondering If a character gain text from a game effect, does it stay for the rest of the game ? For an example, if I call in Rusty, and he hits a opposing character. That opposing gains fire token which gives the text from THIRD-DEGREE BURNS . When Rusty leaves the map beginning of my next turn , does the opposing character keep an active fire token for the rest of the game?

Yes. The way I read THIRD-DEGREE BURNS, the only way to remove the Fire token is by clearing action tokens or by moving through water terrain even if Rusty is no longer on the map.

I do not agree. I see nothing in the verbiage of 3rd degree burns to indicate that the token will have any effects once Rusty is gone.

Tokens/markers have no effect once the game effect that placed them is gone. The rule about Keywords is very clearly specifically for Keywords, it has no bearing on anything else in the game.

same rulings were made by WK for Proxima Midnight's tracer tokens.

If she's not on the map, then the tokens don't "burn".