If you can, disconnect and seperate the wires at the T-stat( mark them
so you know where they go). If the fan shuts off, you have a problem
with the T-stat.
However if the fan still runs, go disconnect the T-stat wire at your
furnace. If the fan shuts off, you have a shorted T-stat wire somewhere
between the furnace and the T-stat.
If however the fan still runs, you have a problem with the furnace.
Perhaps it could be a stuck relay.