What would be evidence for increased temperature affecting plant species in a mountainous region?

If the temperatures are increasing in a mountainous region, in order to be sure in that, the evidence can simply be obtained by the vegetation. The mountains tend to be warmer at the lower parts, and as the elevation increases, the temperature decreases. If it is a higher mountain, then we will see that there is certain type of vegetation in the lower parts, above it a belt of another vegetation type, above that one there's usually a belt of grasses, and the highest parts are usually with little to no vegetation. If the temperature increases though, then the vegetation from the bottom will start moving upwards, occupying larger portion, the second layer will move upwards as well, and the grasses will come around the top part of the mountain, with the barren part disappearing from the scene.