(Warning: unpleasant imagery on the link to follow)
As survivors from Hiroshima and Nagasaki showed, even the lightest of fabric provides enough stoppage from the thermal radiation to project your skin from the brunt of the thermal pulse. This will be an issue if they soak so much heat they start to char and burn of course.... but a pool of water? Oh yes, that will do just fine.
But we are getting ahead of ourselves... your question was as follows:
Would the thermal mass of 2-4 meters / 6-12 feet of water be enough to prevent you from frying?
Yes it would, and the closer to ground zero you are the better. This is because that — even if assuming that the pool would start to boil — it would do so at the top, because the thermal pulse is infrared, which water absorbs easily.
As the pool boils at the top, a layer of steam will form. This will "blanket" the pool and keep the thermal pulse from reaching the water below, like an ablative heat shield.
The reason you want to be close to ground zero is that there the dynamic pressure (i.e. the "blast" part of the blast-wave) will be very little. This would keep any such steam blanket from blowing away.
So surviving the thermal pulse and the heat of the fireball at the bottom of a pool, yes, that will work, and will also keep you from the worst of the radiation pulse. The shock-wave will be mostly reflected, and the blast-wave will be small due to the proximity of ground zero.
This however does not mean guaranteed survival. Here are a few problems you need to contend with.
- The thermal pulse happens fast.
The crux for you is that the peak intensity of the thermal happens near instantly after the blast. Unless your character knows what is about to happen, they will need to be in the "shade" as the detonation initiates. Any thin metal roof will or parasol will do. But it is required that they are there at the moment of detonation or they will be set on fire.
- The fire-storm
Ok, so your character survived the first minute under water. Now they need to come up for air. What are they coming up to?
A hellish burning inferno where the atmosphere is thick with smoke and poisonous gas
Everything is on fire. And even if the worst of the nitrogen oxides have been pulled up into the atmosphere by the rising fireball, you still have a hellish firestorm producing smoke all around you. There is no clean air to breathe, even assuming you ignore the radiation for the moment.
Solution: they are an amateur diver
This may sound far fetched but unless your character is an enduring protagonist, here is an everyday scenario that yours truly have experienced, and that hundreds of thousands of people do around the world every day:
They were practicing scuba diving
Your first scuba dive will most likely be in a pool. Before letting you jump into the ocean, the instructors commonly let you get acquainted with the diving gear in a nice calm pool. Also during certification you may very well do some of the checks in a pool. Proficiency checks, and/or checking the status of your own gear after you have your certificate can also be done in a pool.
A common sight at diving outfits around the globe
This means that your character — at the moment of detonation — can be suited up in a wet-suit, covering them from head to toe. If they are wet from before, even better. This will make them survive the first few seconds of blinding light and searing thermal radiation.
If they have their wits about them, they can just grab a tank, and dive head first into the pool. This lets them stay below for as long as it takes for the worst of the firestorm to abate. Plus they also have an air tank (or several even as they were with other divers) to provide them with air for the initial part of the mayhem.
"Yeah but what are the odds that a random character..."
They were not a random character... they were visiting — or a member of — a diving club. Extremely lucky for them as individuals, yes, but not at all strange when looking at the city as a whole. You are writing about them specifically because the fact that there were divers and doing that at that moment is what saved them from instant incineration.