Come on Max, you're better than this. Global average temperature is a tool to measure indirectly the change in the Earth's energy budget. More to the point, your argument doesn't really seem to be addressing the crux of the issue: the nature of desertification and its relation to climate change. The extraordinary claim that modern climate science is fundamentally wrong on important measures requires extraordinary evidence, after all.
This isn't an extraordinary claim, the coldest periods in the last 30,000 years had vastly more arid landscapes, with deserts spreading enormously. The warmest period in the last 30,000 years was about 5~6 thousand years ago, and the Sahara had grasslands spreading across it.
Take pollen and other plant fossil data and map it:
http://www.bridge.bris.ac.uk/resources/Databases/BIOMES_dataInput the data into a model so you can get a usable example spectrum for how the planet would appear from an exoplanetary system:
https://arxiv.org/abs/0901.1214Scroll down a couple pages to the biome maps they used.
Note that they checked if the model results properly reproduced the known distribution and such of biomes and foliage based on various lines of evidence,
and noted where they did not like the grasslands in australia.This has nothing to do with any claim about climate science itself, it's the sort of thing you only actually find in the "Summary for Policymakers" sections. It's a scare tactic that preys upon people reflexively linking "desert=hot, warmer here=more desert-like, desert life=hard, fuck, that's bad" when it should be "desert=dry" and any further inferences would be changed accordingly.