It may be possible (I am not an expert on furnace issues) that if the low switch is shorted, the furnace "thinks" it is still running. When you shut it down manually at the thermostat you are tricking it into thinking it is starting up cold.
I am not sure where the switches on your furnace are located but they are usually flat,about an inch round and have 2 wires on them. there are 2, a high & low temp. switch I believe they are marked with the temp. setting on them.
"If I can't fix it, I can screw it up so bad no one else can either."