“A 76-year-old man from Kingstanding, Birmingham and a 56-year-old man from Bilston, Wolverhampton have been detained on suspicion of murder.”
Police said she had “lots of friends and acquaintances” and teams were trying to establish if she had any “long-term partners”.
Ms Jerrare lived alone in Heath Town and had lived in and around Wolverhampton for most of her life.
Speaking to the press at the scene on Bridgnorth Road as he made an urgent appeal for information, Det Supt Chisholm said: “What we know about her so far, she led a fairly chaotic lifestyle.
We believe she would have been well known in the Heath Town and Wolverhampton area.
The two men arrested on suspicion of murdering her have been bailed.
Bridgnorth Road has been closed in both directions from Tinacre Hill to the junction with Jenny Walkers Lane with a diversion in place while forensics teams continue working.
A West Midlands Ambulance Service spokesman said: “We were called to an incident at the junction of Jenny Walkers Lane and Bridgnorth Road at 2.49am on Monday, one ambulance, a paramedic officer and a MERIT trauma doctor attended the scene.
“On arrival we discovered one patient, who sadly could not be saved and they were confirmed dead at the scene.”
Detectives also believe she was driven to the site before being set on fire and are now appealing anyone with information to get in touch.
Forensics tests are under way in a bid to identify the woman.
Anyone who may know who she is, or saw anything suspicious in the area is urged to contact police.