Cicerone
The sun is way too hot to burn, even at its surface. It undergoes nuclear fusion from its centre to about 1/3 of its way to its surface. Fusion of Hydrogen starts at about 10 Million Kelvin, Fusion of Helium starts at 100M Kelvin - the temperature of our Sun's innermost core. Fusion is a process that makes heavier particles from lighter elements. The Sun converts Hydrogen into Helium; releasing alot of energy. At the surface the temperature is only 10,000 Kelvin so all gaseous matter is in a plasma state and glowing rather brightly.
JJ,
Temperatures don't so much have ceilings they can introduce phase transitions in spacetime.
There is a challenge to experimental physics attempting to understand the Big Bang and black holes (ultra high energy environments) - it's called the Heirarchy problem. Basically we live in a relativistic framework ruled by four forces and 120 or so extremely well defined constants. The four forces are gravity, electromagnetism, strong nuclear and weak nuclear. If your energy density in an area of spacetime exceeds a certain threshold - that is very, very high - these four forces are theorised to recombine.
As you raise the temperature higher and higher you in theory go from 4 forces to 3 to 2 until you are left with one combined force, called quantum gravity.
The conversions are:
i) 4 -> 3 is electromagnetic and weak nuclear forces combine into electroweak at 100 GeV or 10^15 Kelvin (observed regularily at CERN)
ii) 3 -> 2 is electroweak and strong nuclear forces combine into electrostrong at 10 ^ 14 GeV or 10 ^ 27 Kelvin (unreachable on Earth)
iii) 2 -> 1 is electrostrong and gravity combine into quantum gravity at 10 ^ 19 GeV or 10 ^ 32 Kelvin
As the four forces combine you step away from a region of spacetime with specific physical constants operating under the laws of relativity hold sway. Call these phase transitions.
The most powerful collider yet to enter operation (2007 - the Large Haldron Collider or LHC) targets accelerating atomic particles to a ceiling around 200 - 250 Gigaelectron Volts (GeV). Phase transition two of the four forces should start at 10 ^ 14 GeV, whilst the last phase transition kicks in around 10 ^ 19 GeV.
So the steps are way to large to create on Earth - using colliders you'd need one the size of our solar system to hit the first of these stages.
So as energy densities are interconvertable with temperatures (1/2 mv^2 = 3/2 k * T)
Proof you can work out a threshold temperature where the four forces combine, alah:
You quoted temperature (circa 10 ^ 20 Kelvin) looks wrong because it doesn't align to one of these higher boundary layers.
More here, if you wish to learn about unification theories, and s-particles like gluinos, winos (supersymmetric W's) and zinos (supersymmetric Z's)
More interesting unification science