I'm going to answer this from a whole different angle -- remember, if you allow this dog free access to the outdoors it is NOT going to have common sense about when it has had 'enough'. That's *your* job.
The longer a dog lies in the sun, the more relaxed and 'mushy' brained they get -- often the dog won't even move to GET a drink!!
Please limit this dog's ability to just 'go out'. It feels good -- but they know no logic about "I have to protect myself" and sunblock just won't do it.
Dogs are like children and sometimes they may love something that needs to be limited. A child may like ice cream but letting them have "all they want" is disaster. Please watch the clock and only allow the dog to be outside for short periods of time, closely monitored. Then don't let the dog go back outside ... but keep it inside. If you shut the door the dog will be content - particularly if you supply affection and playing as compensation. But your gentle 'No, you've had enough' will always be the best thing.