Good day Mr. EyEscOLd!
I am a registered nurse assigned in a certain tertiary hospital. Are you sure that your wife suffered from second degree burn (or just a first degree) due to hot pack? What is the rationale of the nurse in application of hot pack? Did the nurse instructed you or the patient to put cover cloth to prevent burn?
As a nurse, we do hot compress (covered with cloth to prevent burn) when the patient is experiencing pain, has inflammation or cannot void. The hot compress is an independent nursing intervention to provide temporary relief to patient's ailments. I guess the nurse is just doing her job and it is not intentional to cause harm to patient. The patient is the one who perceived pain/heat so she must call the nurse immediately. It is also an instinct to remove it when it is too hot. Usually even moderate temperature but prolonged contact can cause burn. You can classify burn as first, second (superficial partial thickness), second (deep partial thickness), third and fourth degree. See http://en.wikipedia.org/wiki/Burn for thorough explanations related to burn.
You can make a written complaint at the hospital. I guess that's just a minor burn and will heal itself in a few days, unless if your wife has Diabetes it will take some time and requires proper care and consultation. If that's not life threatening, so what do you think should be paid for? I hope it helps!