Police have put out a nationwide appeal to help find the victim's name.
He was found by the side of the M45 near Dunchurch on December 30.
Now police are asking "Who haven't you seen since the New Year?"
Click here to see the police video of the appeal.Detective Superintendent Adrian McGee, who is leading the enquiry said: "We are making a nationwide appeal for everyone to think who they haven't heard from, or seen since the New Year, who they would normally expect to.
"This man was somebody's husband, somebody's brother, somebody's father, somebody's friend, somebody's work colleague.
"Friends and relatives tend to meet up or speak to each other on the phone around New Year. Who haven't you seen or heard from?
"Perhaps the person who works next you hasn't returned to work after the New Year break?
"We need you to think whether the person you haven't seen or haven't heard from matches the description of the victim."
The man is believed to be between 5ft 2 to 5ft 6. He had longish wispy hair and distinctive nose and teeth.
The victim also had some facial hair, either long side burns or a full beard, which was dark but greying.
"When he was found the man was naked, although it is not known whether his clothes had been removed, or whether they had been burnt by the flames," added Det. Supt. McGee
It is believed the man was already dead when his body was left at the side of the Eastbound carriageway of the M45 and set on fire.
A passing motorist alerted the fire service to the flames, but on arrival fire officers realised a body was involved and contacted the police.
A Post Mortem examination has established the man suffered substantial head injuries and was dead prior to his body being set alight.
Police are still wanting to hear from anyone who was driving along the M45 on Tuesday, December 30 between 12.30-1.30pm.
"We know that traffic was fairly light on the motorway around that time and we are asking anyone who was travelling in either direction on the M45 at that time to contact the incident room," said Det Supt McGee.
The incident room can be contacted on 01926 415789, or by email on incidentroom@warwickshire.police.uk
Or contact Crimestoppers on 0800 555111 where the information can be given anonymously.