I think reading climate change into Biblical texts is stretching the text to fit what we're seeing around us.
In the OT there certainly were all sorts of plagues and famines and things but they were brought to bear against specific situations. You wouldn't see a situation where Israel fell into sin and as a result the Assyrians were punished with flooding.
The sun burning men (Rev 16:8) is the result of the angel pouring his bowl upon the sun, and doesn't appear to happen until the first three angels have done their things with their bowls. The first angel's bowl caused loathsome sores to break out on those who had taken the mark of the beast; the second and third angels turned the seas and rivers to blood. Since neither of those have happened yet it's probably safe to say the fourth angel hasn't poured his bowl out.
That's even without getting into a discussion of whether Revelation describes a sequence of events or multiple things going on at once