What is the fundamental reason for death from too high or low internal temperature?
As mentioned in the comments, half of your question is answered elsewhere. Generally you are right, different processes change at different rates. Blood viscosity changes. Some complex systems, such as the heart, may completely fail to function. The other half of your question has a simpler answer. As heat increases, yes in theory so should enzyme performance. However enzymes have a tendency to denature if they get too hot. When heat is excessive, heat shock proteins are released which are naturally stable in hot conditions and which attempt to stabilize other proteins. This is only possible up to a limited extent, and sufficient heat will cause proteins to become entirely non-functional.