The post in question writes "have risen higher", which to me reads as if it's saying that the temperature, as a result of rising, is now higher than ever before

The post in question writes "have risen higher", which to me reads as if it's saying that the temperature, as a result of rising, is now higher than ever before, not that the rate of change is higher. I would expect something along the lines of "have risen faster" if we were describing the slope of the graph of temperature over time.