I think the warmest water is typically going to be desert areas within or near the tropics. Especially coastlines that have protected, shallow coves.
Being at or near the tropics is fairly obvious, being that you will get a strong, overhead sun all year, and you get relatively long days all year round.
But, I think being in a desert helps greatly too, because you get lots of sunshine, and high air temperatures. If an area has shallow, protected coves, you get stagnant water, where the surface can really heat up and is not replaced by cooler upwelling water during times of wind or storms.
If you move outside the desert areas, and get closer to the equator, you will get a lot more cloudiness, which will prevent the sun from really heating that water. We would also probably exclude desert areas on the western coasts of continents that are directly exposed to cooler waters circulating from polar regions (west coast of southern Africa, west coast of South America, west coast of southern Australia, etc...). These areas might meet the other criteria (desert, near tropics, shallow coves), but because they are being fed cool water from the polar regions, the water can only get so warm.
I think the places that meet the criteria for the warmest waters (desert near the tropics, lots of coves, not exposed to circulating polar waters) are going to be in the Red Sea and Persian Gulf, Gulf of California in Baja, Mexico, and North Western Australia. I believe of these, you will find the highest temperatures in the Red Sea and Persian Gulf.
Quatar (Persian Gulf) August high: 95.3 (
Al Wakrah Sea Temperature August Average, Qatar Water Temperatures)
Djibouti (Red Sea), September high: 90.1 f (
Djibouti Sea Temperature September Average, Djibouti Water Temperatures)
Loreto, Baja Mexico, August high: 89.2 f (
Loreto Sea Temperature August Average, Mexico Water Temperatures)
Darwin, Australia: March high: 89.8 f (
Darwin Sea Temperature March Average, Australia Water Temperatures)