I have a very old house and the two wires to my thermostat are white and black. I hooked the white to W and the black to R. I got heat, but the heat did not turn off and continued to run even after the temperature far exceeded what the thermostat was set at. Could it be that the I attached the wrong wires to the W and the R. Thank you.

Depending on the t'stat model, there may be a jumper on heat only-2 wire units. See if there is a red jumper wire between Rc and Rh. Disconnect the jumper and try again. Let us know if it works.