What will the climate be like in Northern Hemisphere if the Amazon rainforest turned into a desert?

It would depend on why the rain forest turned to desert. It would require some drastic change. Actually a number of drastic changes all occurring at the same time. One requirement would be mive uplift in the Andes. Since the Andes are already pretty high and the Amazon is still wet, we're talking MIVE uplift. That kind of tectonic activity would probably be accompanied by a lot of volcanic activity - enough to trigger another ice age. So the result (in this thought experiment) would be to make the entire northern hemisphere very, very cold.