There are varying accounts from the middle ages but during the US revolution Pine Tar was used, not the "tar" most people think now with road crews and asphalt (syrup and cat tails were used if supplies were nto available). But the Pine Tar was heated, boils around 135-145 degrees which isn't too bad, but considering back in the old days it would be heated by camp fire or Franklin Stove, don't know how accurate you're going to get the temperature. Some accounts make no mention of the application, while others mention boiling and blistering of the skin on application.
One of the most brutal accounts on record though was the Second tarring and feathering of John Malcolm. Ship Captain, British Officer, British Loyalist and Customs official who very much loved his job. The first time he was tarred and feathered it was over his clothing which is considered a more "gentle" act of public humiliation and punishment. The second one was quite different. He was witnessed in an altercation with a young boy and threatened to strike him with his cane. A local Patriot shoemaker, George Hewes, intervened. Malcolm told him to stay out of it and "Not to interfere in the business of a Gentleman". Hewes replied that at least he had never been tarred and feathered, to which Malcolm struck him in the forehead with his cane and knocked him cold.
Now John Malcolm wasn't the most liked guy. He had traveled North Carolina during the War of the Regulation. Kind of a Revolutionary War "light", lasting from 1765 to 1771 where North Carolina citizens took up arms against what they viewed as corrupt officials. John Malcolm took great pleasure in subduing some of the uprisings, adding in his tax collection and customs work and the all around general reports of how much he loved doing his work... Well, not going to make you many friends in places like the Colonies.
Later that night after he knocked out Hewes an angry mob formed outside his house. Rather then back down he egged the crowd on, shouting "You say I was tarred and feathered, and that it was not done in a proper manner, damn you let me see the man that dare do it better!”. The mob was agitated by that, partly due to a previous occurrence where another British Customs officer had killed an 11 year old boy and escaped punishment due to a Royal Pardon. So, frustrated even more they most likely decided to take that frustration out on him.
He was taken from his home, stripped to the waist and marched to King Street. Hot tar and feathers were applied and then he was marched to the Liberty Tree and ordered to apologize for his actions and also renounce his commission. He refused, even when a noose was placed around his neck and he was threatened with Hanging. He again refused, reportedly relenting only when the mob threatened to cut off his ears.
I'll put the next part in spoilers since it's a bit on the gruesome side and not many want to read things like that
After the attack he left the Colonies and went to England. During his travel home he kept a box, in which he kept his skin which had "peeled off in chunks" from the hot tar, to which he showed King George III to show proof of the suffering he had endured for the crown