The conditions that crops need aren't based on average temperature, but rather they're based on the minimum temperature, the maximum temperature, and how long it takes to go from very cold to very warm and vice versa. With global warming the climate zones don't just shift north, but rather you get these situations where certain crops just won't grow at all. For example, grape vines have certain mechanisms to protect the buds during winter, but these mechanisms get disabled as soon as you get the first warm snap. The problem is that if it then gets cold again you lose all the buds, so no grapes.
With global warming what happens is you still have very low minimum temperatures in winter, but the average temperature is warmer and so you have these temporary warm snaps disable all the natural protection mechanisms that have evolved over thousands of years. So if you just move the vines north then they all die because their cold protection mechanisms get disabled and the buds freeze, and you can't keep them where they are because it's too hot in the summer so they die also. So what happens is that you just can't successfully grow good wine grapes anymore. Now obviously this is a pretty trivial example, but there are similar things going on for a lot of our major food crops. You can't just move them north, so we're just going to have major food shortages.
Another good example is wheat rusts. Every winter our top scientists go down to Mexico and create new types of wheat based on whatever rust is currently spreading. The only reason they have time to do this is because the wheat sprouts later in the US than it does in Mexico. But with global warming all the wheat will come up much closer together, so what may happen is that we just don't have wheat anymore.
(And believe me, wheat rust is pretty much the scariest shit you can imagine. There's a reason it was one of the biblical plagues.)