All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The jurists differed in opinion about the ruling on guaranteeing a borrowed item if it is damaged or lost while it is at the hand of the borrower. Ash-Shaafi’i and Ahmad are of the view that the borrower is obliged to guarantee the item whether or not he is negligent about its damage or loss. However, Abu Haneefah and Maalik are of the view that the borrower is not obliged to guarantee the item unless there is negligence or transgression, negligence is related to preserving the item and transgression is related to using it.
The most preponderant opinion –Allaah Knows best –is the first opinion, because the Prophet borrowed some shields on the day of (the battle of) Hunayn from Safwaan ibn Umayyah and then Safwaan asked him: “Are you taking them (shields) by force, O Muhammad.” Thereupon, the Prophet said: “Rather, it is a guaranteed borrowed item.” [Abu Daawood]
Furthermore, Samurah narrated that the Prophet said: “A hand is responsible for what it has taken until it gives it back.” [Abu Daawood and At-Tirmithi]
Ibn Qudaamah said: “This is because he (the borrower) took the property of others for his own benefit while benefitting from it by himself only, without deserving it and without permission in causing damage to it, so he guarantees it just like a usurped item or something that is taken for trial when one wants to buy it.”
Therefore, the owner of the borrowed item has the right to ask for guarantee, and the person who borrowed the item is obliged to guarantee it whether or not he misused it.
In the situation given in the question, what should be done is what is known in the custom of the jurists as Arsh (monetary compensation), which is that the car should be valued before the damage (the burning of the engine) and it should be valued as well after the damage, and then the borrower is obliged to pay the difference between the two values.
Allaah Knows best.