Earth’s global temperature has changed greatly in the past hundreds of years. This is due to how much energy the planet is receiving from the sun and how it radiates back. Another cause is humans, due to deforestation, burning of fossil fuels, pollution, etc.
A higher temperature gradient causes faster heat transfer, and thus faster convection currents. If the core were cooler, the temperature gradient would be lower, so the convection currents would likely slow down.