Charlie and the Perplexing Temperature Billboard

RAY: This puzzler is from my Fahrenheit-Celsius series. It's from Mike Mercer, and I didn't really even have to obfuscate this at all! Here it is:

Charlie is heading off to work one fall morning, and as he does every morning, he passes a billboard that displays the current temperature in Fahrenheit in one corner, and the temperature in Celsius in the other corner.

He notices both temperatures, and thinks, 'It's a pretty nice day for late fall.' But, as the day progresses, a monstrous cold front hits town. On his way home, Charlie passes the temperature billboard again, and finds that the Fahrenheit temperature is now 36 degrees colder than it was that morning. So, when he drove in it was one temperature, and now it's that temperature minus 36.

But, when he looks at the Celsius temperature he's confused, because it reads exactly the same as it did that morning. Charlie figures that the display must be stuck, because it's certainly much colder on his ride home.

In fact, it was not stuck. But, there was indeed something wrong with the Celsius sign.

What was the problem and how cold was it?

Think you know? Drop Ray a note!