Your circuit board should have a little red light that flashes in a repeating patern, on the backside of the blower compartment door is a legen detailing what that code means, if no legend Google it. By turning the heat off and back on that resets the ignition module and this is what I suspect however it is too premature at this point to say so, the fact as you mentioned the fan blows cool tells me the temperature delay is hanging up too?
Notice in heat mode the low speed fan is used, this is operated by the temperature delay usually and not the thermostat,
The temperature delay / high limit safety is a combination device located just above the burners.
The thermostat controls the high speed which is the cool speed as well as the fan "on" speed.
I tried to post pics of the high limit/ temperature delay as well as the induced draft proving switch, the proving switch is often an issue if the barbed port on the induced draft assembly to which the proving switch's rubber tubing attaches gets clogged requiring a reaming to clear.
Google both devices as it appears I could not get the last 2 pics to show up.
Notice in heat mode the low speed fan is used, this is operated by the temperature delay usually and not the thermostat,
The temperature delay / high limit safety is a combination device located just above the burners.
The thermostat controls the high speed which is the cool speed as well as the fan "on" speed.
I tried to post pics of the high limit/ temperature delay as well as the induced draft proving switch, the proving switch is often an issue if the barbed port on the induced draft assembly to which the proving switch's rubber tubing attaches gets clogged requiring a reaming to clear.
Google both devices as it appears I could not get the last 2 pics to show up.