Ok, so the weather is hot in Phuket and you feel the need to take you shirt off in public, but is it OK to do this in Thai culture? It is and it isn't and it all depends on where you take your shirt off.
It is OK to take you shirt off down the beach, as the beach is the place where you take your shirt off for a swim and it is OK to walk around all day like this at the beach. Even though most tourists come from the beach and haven't bothered to put their shirt back on, this is frowned upon by most Thai people, but they just accept it.
Most people wouldn't walk around the streets without a shirt in their own countries, but do it everywhere in Thailand and don't have a care in the world for their culture. It can be offensive to some Thai people, to walk around the streets with no shirt on, but as mentioned before, the Thai's will just tolerate it as so many tourists do it.
It's pretty offensive in any culture for some fat sweaty man to be sitting down to eat at a restaurant and you will see this at every tourist destination in Thailand. Why some think it's OK to do this in Thailand, is anyone's guess.
Believe it or not, the police can actually fine you for not wearing a shirt and have done this before. It all depends on what mood they are in for the day and how much revenue they feel like making. It is very rare to get fined for not wearing a shirt, but it does happen.
If you wear no shirt in a shopping mall, it is just as offensive or even more so than doing this in your own country, so it is advised to not do this at any time.
Once a lot of guys get to Thailand, they seem to not care about what anyone thinks and just do as they want and it's this kind of attitude that can get some into trouble. Basically, don't do in Thailand what you wouldn't do in your own country and you will be fine and for the sake of not offending any of the locals, it would be best to keep your shirt on, if you are anywhere other than the beach or the pool.