Is there a limit to how hot an object can get?

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.

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