Come on man, you KNOW why we can have high confidence in a trend even if we can’t predict the exact temperature 5 days from now. It’s the same reason you invest in the stock market even though you can’t predict exactly what the price will be 5 days from now. It’s a very basic statistics concept that your confidence in an overall trend can be extremely large even though your concept in any one sample is small.
We know that the temperature has been going up very obviously, very dramatically, and very recently, coinciding exactly with our carbon output. I think the fact that Earth has gone through multiple eras such as the ice age shows it doesn’t really care about “healing itself” (which, by the way, is a complete misnomer, since Earth doesn’t really care how hot it is — WE do). If such a mechanism exists, then let me just say, it sure is taking its sweet time to get to work!