It will depend upon the coverages that you have on your car whether it being stolen and set on fire will be covered by your auto insurance policy or not. You would need comprehensive insurance on your vehicle in order for it to be covered for both the theft of it and the act of vandalism which someone did to set it on fire.

Comprehensive covers your vehicle for losses other than collision (OTC). This can include covering for your car if it is stolen, damaged by flood, fire or animals among other things.

If you have comprehensive coverage on your vehicle you should place a claim with your insurance provider. Unless the thieves were caught by police it is likely that your insurer will do a thorough investigation into the vehicle being stolen and destroyed by fire before settling a claim for this type of total loss.

In cases where a car cannot be repaired an insurance company will determine the vehicle to be a total loss. When this occurs the insurance carrier will calculate the actual cash value (ACV) of the vehicle in the condition it was in before being stolen and set on fire.

This article on the Simple Steps to Filing Your Car Insurance Claim may be of use to you at this time as you contact your agent to find out about making the claim for your stolen vehicle.

If you only had liability coverages on your vehicle then you would not be covered. Liability covers only those you may cause harm to in an accident, not protect your car in any way from collision or claims for it being stolen and set on fire.