Transient geotherms
Instantaneous heating or cooling

The cooling of a dike with half width w is another problem which has an analytical solution in the following form:
If the dike has a width of 2m, i.e. w=1m, and its initial temperature was Ts=1000°C, and κ = 10-6m2s-1, then the temperature at the center of the dike would be about 640°C after one week, 340°C after one month, and only 100°C after one year.
Some swarms, such as the giant McKenzie swarm in Canada, appear to radiate from a point, commonly interpreted as a plume source for the magmas. The mid-Proterozoic Coppermine River flood basalts were erupted at the same time near the plume head. Individual dykes range from 10-50 m in width, with some up to 200 m wide. Some dykes can be traced for up to 2000 km.