Check at the air handler to see what terminal the Blue wire connects to. Sometimes it may be the Common. If your thermostat has no C (common) terminal (battery powered) then leave B disconnected.
Usually when the Aux heat is called for there's a relay with a 24 volt coil switching the 240 Volt power used for the Aux heat. I am assuming you have heat strips. It's possible the coil is shorted causing the fluse to blow when voltage is applied to the coil when there is a call for Aux heat. Check the control board for any signs of discoloration due to excessive current flow.