With your own vehicle it is possible to travel from the country where the vehicle is registered into Thailand, assuming you have paperwork to prove vehicle ownership and insurance and you drive to Thailand at an approved border crossing.
From Malaysia, one can cross from Bukit Kayu Hitam into southern Thailand. If you need visa paperwork, immigration paperwork is available on the Malaysian side of the border. The border closes at 10pm Malaysia/9pm Thailand time.
Those with cars registered in Laos and Cambodia can cross into Thailand at approved checkpoints including Nong Khai, Mukdahan, and Aranyaprathet.
It is not generally allowed for tourists to drive rental vehicles from a neighboring country to Thailand.
Before driving to Thailand please get additional information at www.customs.go.th and www.mfa.go.th