(Before anything, I'd like to apologize for my sketchy English, it's not my primary language)
As you said, it must be a hardware problem. Usually, a heat sensor is printed in your graphic card's circuit boards. You are looking for a thermistor, wich should basically look like a small ceramic ball (probably black) usually labeled TR-000, numbers vary depending on the model
Normally, you should have two Tin drops closeby the said thermistor. If you can't see any, your sensor isn't powered, therefore it's not well.. sensing. You can fix that by using a Tin wire, that you heat until it's liquid. I'm quite certain you know how electricity works, basically it's a missing link. If it's not one of the drops, you should notice a burn (it could...