This is a really old unit who's brand name hasn't been used since the late 60's or early 70's, I believe. I suspect that the combination fan/limit switch has failed in the 'on' position. This would be a common failure mode, and it's a relatively cheap part and easy to install. Parts for these units are available from Lennox/Armstrong brand dealers, since Armstrong is what G&F is now.
"Nothing is foolproof to a sufficiently talented fool"