Do I have a case?

You *may* have a case for liability--i.e. for showing that they are obligated to pay for your injuries--if you can show that the injuries were due to too-hot (inappropriately or unreasonably hot) liquid, which you seem to feel you can show.
But that then leaves the second part of a worthwhile case: damages, or what compensation you are owed. You can only recover compensation for 1) your out-of-pocket (not paid by insurance) medical costs due to the injury; 2) lost wages due to the injury (if any); and 3) for *significant disability or life impairment lasting *many* weaks or longer, some amount for "pain and suffering." The pain and suffering award is usually more or less proportionare or related to the medical costs: if the injury was not serious incur to large medical costs, there will likely be little in the way of pain and suffering compensation. 
At the same time, if you have to sue (i.e. if they don't voluntarily offer you compensation), you'd have to hire a medical expert (i.e. doctor) to testify as to your injuries and the treatment of, and hiring such an expert can be expensive. Therefore, if you--as we hope--have recovered well, with no lasting detriment and did not occur large medical costs, then it would not be worth taking legal action.
If you did incur large costs or suffered lasting disability, significant scarring, etc., it would be worthwhile to consult with a personal injury attorney about your case (many such attorneys will provide a free initial consultation; you can inquire into this before making the appointment), to see if it's worth pursuing.