Generally speaking, if the stovetop in this scenario is not defective and it was installed properly, but the tenant or one of the tenant’s guests burned himself or herself while using it, then no, the landlord is not responsible for damages.
Liability in tort requires duty, breach, damages, and causation. Unless there is evidence that the landlord breached an identifiable duty, and the burn was caused by this breach, then there is no tort liability. The fact the landlord ultimately owns the stovetop does not make him or her the insurer of all persons who may injure themselves whiles using it.
That said, if the stovetop was defective or its installation otherwise constituted a danger, it’s possible the landlord may share liability for resulting injuries.
This is a blog post, not specific legal advice. No attorney-client relationship is intended or created.