Full thickness burns are not painful, but no one with an extensive burn has pure full thickness. Where you have a full thickness burns you will typically also have a lot of partial thickness, which are extremely painful. A burn is probably the single most painful injury it is possible to have. I have seen some horrendous ones, and the screams of the patients and the smell will stay with me forever.
At this stage, if he were still alive, the pain from the burns would be the least of his issues, as he would almost certainly be septic from the untreated dead tissue, with the infection spreading through the eye socket to the brain.