Is there a limit to how hot an object can get? If heat is the measure of how fast the atoms are moving in an object, than isn't there a limit to how hot that object can get as nothing can go as faster than the speed of light. So because the atoms can't vibrate that fast, will there be a limit to how hot the object can get?
 A: Wikipedia says:

Above $1.416785 \times 10^{32}~\rm{K}$, all theories break down. So, that is the theoretical limit.

In actuality, $7.2$ Trillion°F is the highest known temperature, and that temperature was achieved in Large Hadron Collider (LHC) when they smash gold particles together.
In terms of the motion of atoms, the limit would be much lower because the atoms will fly away as a gas. Higher temperatures can be achieved by containing the atoms from flying by compressing them at high pressures. At some point, the compressor will also blast, or evaporate.
One way it can reach very high temperatures is where the heated matter also provides its compression. That can happen when gravity itself creates compression so that there is no problem of the blast or evaporation. May be temperatures at the time of big bang, or that of a singularity.
However, the main problem would be that of measuring such temperatures, so, the temperature would be limited by the range of the measuring mechanism.
A: There's something called the "Planck Temperature" that is the current limit of how hot something can be before the physics we use to describe it breaks down.
The Planck Temperature is about $1.4 \times 10^{32}~\rm{K}.$ 
Above this temperature, we can't describe the behavior of a substance because we don't have a working theory of quantum gravity. Of course, $1.4 \times 10^{32}$ is many orders of magnitude hotter than anything in the Universe, so it's really only a theoretical limitation and only comes into play when we're trying to describe the nature of the universe immediately after its formation. Within a millisecond after the Big Bang, everything in the Universe was below the Planck Temperature 
and there is a limit to coldness too!! 
yes. its called absolute zero. Nothing can get colder than that. The temps are 
$−273.15$ on the Celsius (centigrade) scale.[1] Absolute zero is also precisely equivalent to $0 ^\circ ~\textrm{R}$ on the Rankine scale (also a thermodynamic temperature scale), and $−459.67^\circ$ on the Fahrenheit scale 
A: The reason why nothing can get hotter than the Planck Temperature is because of the Planck Length, about $1.6\times 10^{-35}$. When there is heat, light waves are given off from the energy being released. We can see the heat from most things unless it is hot enough, and something like fire is. The reason why we can't see human body heat is because the human cannot register the type of light given off. Infrared cameras can see this type of light, so we can see human heat from these. The waves given off get smaller and smaller as the heat goes up and up. This is why the Planck Temperature is the highest, because the wavelengths become as short as the Planck Length, and as the answer above says, nothing with mass smaller than the Planck Length can exist in the physical universe.
