Sorry no, the C rating is not the temperature.
I think it is a rating for continuous current ability or something like that. I *think* the higher the number, the more current it can provide.
I don't know if it means more current it can provide OR more current it can WITHSTAND (i.e., if you draw beyond that, then it blows up or something).
And I don't know if it applies in reverse for recharging, whether higher C rating allows you to recharge at a faster rate with more amperage (?) without danger.