Have done this many times.Â
You need to get additional insurance to drive in Thailand from the company that has the policy for the car. You can buy it from agents near the border but it is best to get it before you leave. Its about RM70 for about 15 days. I dont think you are eligible to stay longer than 15 days at any one time. Some European countries can now stay 30 days when crossing a border by car.
The drive from KLCC to the border at Sadao is at least 6 hours (on main North-South Highway) but you can also cross at Betong (sorry to say there was a bomb attack there a couple of weeks ago). Don't cross further east as there can be attacks. There have also been bombs at Hat Yai. We normally drive to Penang Island and stay overnight. The tolls to Penang are about RM60 each way. There are additional ones from Penang through Kedah to the border but they are very low (none in Thailand). We leave about 8 am next morning (be careful leaving any earlier as there are frequently accidents in the dark as there are lots of lorries on the road).
It is heavily policed at the border. You first go out of Malaysia and they check all your papers carefully and stamp you out. You then go through a police check point and have to stop and let them decide whether they want to search your vehicle. Then you drive on to the Thai border. Indian nationals can get a visa on arrival I believe. Check this out.
At Sadao you need to turn left before the border and park the car. Go to the building and get the number of immigration forms you need and fill them out. Go through immigration first. Once you have done this you go the area which deals with importing vehicles into Thailand (yes you have to import it temporarily). The immigration officer fills in a database with your details (first time) and then prints out a form. This takes place in one window. Next you go to the next window where they get you to sign the form and give you a receipt (don't lose this or you wont get your car out) again.
There can be queues from coaches crossing at Sadao as it is the main link to Bangkok (best also to avoid the border Friday to Sunday. Once you get your papers done you just get back into your car and drive out of immigration. When you come to the customs area you dont have to stop - just drive through (it is a detour). Its for lorries to declare their loads (unless you have something to declare). After that it is plain sailing.
If you dont want to actually go to Ko Samui as it is not all that good, you could take a look at Khanom which is on the mainland at the same level of KS. One place to consider would be CC Beach Bar and Resort.
It's about 5 hours from the border to Khanom. You have to get a ferry over to the island of KS, so probably best to stay on the mainland and get the ferry the next day.
Fuel is about 50% more expensive in Thailand so its good to plan your tank contents and fill up in Malaysia before crossing the border. Same on return trip - buy a full tank once you get back over the border into Malaysia. There are two or three stations around the border each side - dont miss them on the Malaysian return side as there are none afterwards until Bukit Mertajam (Penang).
Drive carefully in Thailand and dont break any laws. Foreigners are always in the wrong, regardless of the circumstances and also be prepared to be stopped by traffic police and asked to show your insurance for Thailand.
The style of driving in Thailand is different. Often vehicles will enter the traffic flow by joining the road on the hard shoulder without stopping. It is quite a good system and the drivers are normally very disciplined (better than Malaysia), but it is a bit of a surprise when they just come out of a side road in front of you. There is also a system that when it is safe to turn left, even though the traffic lights are on red, it is permitted to turn. In the numerous small towns along the route there are usually a lot of tuktuks which can be a bit of a bother as they stop suddenly.
Its also important to check which season you want to travel to KS and area as there are monsoon seasons.
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