I've done several 1200 and 1000km events in weather ranging from full sun to cloud and rain. Sunburn can happen even when it is cloudy.
I have found on all the events that once my tights go on, and a long-sleeve top, they rarely come off. It just seems to be a natural response to preventing sunburn.
I have been burnt quite a lot on other rides. I think the worst part is the evening, when I start to feel really chilled even though the skin is red and hot. That takes a lot of energy out of me.
I possibly will be riding in the tropics soon, and I have noted the use by other touring cyclists of cotton, long-sleeve business-type shirts (easily picked up at a Salvos/Good Samartins) and long pants. But the feature of all garments has been the larger fit to allow air to circulate inside (and probably evoporate sweat directly from the skin as an additional cooling aid.
I have a picture somewhere (on another computer) of how a couple cut out the brims of straw hats and gaffer/duct taped them to their helmets as effective sun barriers.
Just while we are on the subject, and as a randonneur who does a lot of night riding, why not consider riding more at night when it is cooler, the sunburn factor doesn't exist, the traffic is much, much lighter, and the scenery possibly is not worth seeing, anyway?
As jamawani says, it's better to be under the shade of a tree next to a stream, than battling it out in hot temperatures.