I think I know the problem but before I risk life, limb, and property, I thought I should run it by someone else.

My blower went out last winter and I had it replaced by a local company. I took me quite a while to realize that it now never shuts off. I thought it might be the thermostat, so I replaced it today but the blower just keeps on running (even with the thermostat disconnected).

I think that the technician mistakenly connected the wire from the transformer to the white terminal instead of the red. If you look closely below the screw head, it looks as if there was previously another wire soldered to the red terminal in addition to the one from the thermostat.

Attachment 4322

Here's the schematic indicating the connection I think is missing:
Attachment 4321

If this I am correct, can I just unplug the unit and switch the wire from the transformer to the red lead?

I believe this to be the transformer:
Attachment 4324

Here's the automatic gas valve for whatever that's worth:
Attachment 4323

This is wired correctly, that is the transformer that the different colored wires are connected to, the one marked transformer is a fan switch for heat, the fan relay may be bad or fan switch out of adjustment.