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"[Leo's] whole body was wreathed in fire. Rain hung in the stormy air, but it only sizzled and steamed around him" (BoO, Riordan 387).

"Rain sizzled and steamed around him." So, Leo's flames would need to be hot enough for water to immediately evaporate anytime it gets near him. We know the boiling point of water is 212 °F (100 °C), but that changes with altitude. "As they ascended, Jason gathered the wind and clouds around him." 6,500 feet is the average for low-hanging clouds. This matches with what is happening in canon ("If they gained any more altitude, the air would be too thin to breathe" (BoO, Riordan 389).), because while there is less oxygen, a person can still breathe easily at that height. A lower atmospheric pressure actually decreases the boiling point, so Leo's heat would be at least 199.6 °F (93.1 °C). So this is the starting point/baseline of Leo's fire in this scene.

"Gaia crumbled to sand, only to get blasted by more flames. Her body melted into a lump of glass, shattered, then re-formed again as human" (BoO, Riordan 388).

Now Leo's heat has reached the point where sand gets turned into glass. This is a MASSIVE jump from the last measurement! For sand to instantly turn to glass, the temperature would have to be at least 3,000 °F (1,650 °C). If materials like soda ash and limestone were mixed in with the sand, that could reduce the melting point to 2552 °F (1400 °C), but that is still CRAZY hot!

"Leo looked like he was made of fire. Flames rippled beneath his skin, illuminating his skull. Leo grinned, which was unnerving in the flames, his teeth like molten silver ingots" (BoO, Riordan 389).

This is a fascinating passage, but it's very hard to break down, due to its fantastical nature. To find a temperature, I searched up, "at what temperature would bone glow?" The result was at least 500 °C (932 °F), but we already knew that, so this isn't a very reliable gauge. Additionally, Leo is highly resistant to heat, so there really is no telling how hot he is in the moment (no, brain, I will not make a 'Hot Stuff' joke, this is a scientific report).

"Festus became an indistinct ball of fire in the sky – a second sun – growing smaller and hotter. Then, in the corner of Jason’s eye, a blazing comet streaked upward from the ground with a high-pitched, almost human scream. Just before Jason blacked out, the comet intercepted the ball of fire above them. The explosion turned the entire sky gold" (BoO, Riordan 389).

So throughout this, Leo's temperature has been growing, but we don't know at what rate. He seems to be alive until the onager's flame joins the mix, so to get the best guess, we'll have to find the highest estimate of the onager's fire. As described in Nico's chapter XLV; "the projectile was a mixture of incendiaries and Imperial gold. Even a small amount of Imperial gold could be incredibly volatile. Exposed to too much heat or pressure, the stuff would explode with devastating impact, and of course it was deadly to demigods as well as monsters" (BoO, Riordan 344). This is also very hard to find a specific temperature for, because there is not much to go off of. But there is one part, "anything in the blast zone would be annihilated – vaporized by the heat" (BoO, Riordan, 344). "ANYTHING." I doubt Nico was thinking of extremely heat resistance elements like Carbon or Tungsten, but we can at least find the 'vaporization' point of materials common to Camp Half-Blood structures. Most common is wood, and then there's marble, melting at 1,339°C (2,442°F), and for Cabin Thirteen, obsidian, melting at 2,000 °C (3,632 °F). Obsidian is probably the material with the highest melting point, so we will use that as our lowest-heat for the onager.

Okay! To get the final lowest estimate of the heat, we need to find the average between Leo's fire, and the onager's fire. The highest measure we found for Leo's fire was 3,000 °F (1,650 °C), when he turned sand-Gaea to glass. The highest measure we found for the onager's fire was 2,000 °C (3,632 °F), the melting point of obsidian. 3,000 + 3,632 / 2 = 3,316.

So, the lowest estimate of the final temperature that destroyed Gaea AND Leo is 3,316 °F, or 1830 °C.

This is PRETTY HOT compared to the average heat of lava, which is 1,000°C (1,830°F)! Or even the highest temperature ever recorded from a rock on Earth's surface, 2,370 °C (4,298 °F), (Scientists determined the temperature by studying a mineral in the rock. The common mineral zircon transformed into cubic zirconia, a process that requires a minimum temperature of 2,370 °C). And this is just the lowest estimate, since I am OBVIOUSLY no expert!

"LEO WAS DEAD. He knew that with absolute certainty. He just didn’t understand why it hurt so much. He felt like every cell in his body had exploded. Now his consciousness was trapped inside a charred crispy husk of demigod roadkill" (BoO, Riordan 419).

And of course, we know that Leo did indeed die from this heat, so our fiery hero is NOT 100% fireproof! Even the pyrokinetic demigod from the Prophecy of Seven has his limits.

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My personal headcanon is that there is NO limit to Leo Valdez's fire, only to what his mortal body can actually take. So if Leo's fire was in the hand's of an immortal being, it could destroy the entire world and never run out.