No, normally the coverages you listed of Uninsured/Underinsured Motorist Bodily Injury (BI) and Property Damage (PD) would not cover your vehicle if it caught on fire.

Uninsured/Underinsured Motorist (UM/UIM) bodily injury obvious would not be able to help you since it would cover bodily injuries. These bodily injuries would be suffered due to an accident where the at-fault party was uninsured or underinsured. Uninsured Motorist usually covers you, the insured members of your household and your passengers for bodily/personal injuries, damages or death caused by an at-fault uninsured or hit-and-run driver. If you are involved in an accident where the other driver is at fault but has no insurance, your policy will cover your medical expenses, up to the limit on your policy.

Underinsured Motorist Bodily Injury covers you, the insured members of your household and your passengers for injuries, damages or death caused by the negligence of a person with insufficient insurance. If you have an accident with a person whose coverage cannot meet your damages, your policy will meet the difference-up to the limit of liability listed on your policy.

UM/UIM Property Damage coverages cover your vehicle for damages it sustains due to an uninsured or underinsured driver that is at fault. Your car is not covered for other acts, such as if you were at fault in an accident or other than collision (OTC) acts such as theft, vandalism or fire.

Uninsured Motorist Property Damage (UMPD) covers your auto when property damage is sustained by an insured and the negligent operator does not possess insurance. Underinsured Motorist Property Damage covers when property damage is sustained by an insured and the negligent operator possesses insurance, but the limits of liability carried by the negligent driver are not sufficient to cover the damages.

So for a fire to your vehicle to be covered by covered by your auto insurance you would need Comprehensive coverage on it. Comprehensive covers your vehicle for losses resulting from incidents other than collision. For example, Comprehensive insurance covers damage to your car if it is stolen; or damaged by flood, fire, or animals.

You can discuss with your agent what covers you do have. If you do have Comprehensive than you should be able to make a claim for your car that caught on fire while parked. The claims adjuster would than investigate and try to determine the cause of the fire and if it was covered by your coverages.