Electrical wire to transmission

I just reinstalled the 273 in my 67 Dart, and I was hooking up all the wires when I came across something I was not expecting. I have a wire that looks like it goes from the starter relay to my automatic transmission. It is grayish, brown or tan in color. Is this correct? And if so, what is its purpose?

It looks like it spent a few miles getting acquainted with my exhaust pipes. Whoever wired this thing left about two extra feet wrapped around my transmission cooling lines. I was glad to have a little extra, but I just wish it woul have been done right so that it would not have even been and issue.

Thanks for any help!