Does Nitrogen dioxide change colour if we put it in a constant temperature of e.g. 100 kelvin?
The changing color of $\ce{NO_2}$ is because it exits in equilibrium with $\ce{N_2O_4}$ as shown in the following equation $$\ce{2 NO_2 &lt;=&gt; N_2O_4} + \mathrm{58~ kJ/m}$$ $\ce{NO_2}$ is a reddish-brown colored gas, while the $\ce{N_2O_4}$ is colorless.  Considering Le Chatelier's principle, 


Taking heat out of the equilibrium will push it to the right
Putting heat in, will push it to the left
Increasing pressure will push it to the right


As we shift the equilibrium we change the concentration of the components, and consequently the color of the gaseous mixture.  

Back to your question, in the solid state (which is where it would be at 100°K), the equilibrium is shifted completely to the right.  So if we had a tube of gaseous $\ce{NO_2}$ and $\ce{N_2O_4}$ at room temperature it would have a distinct red-brown color.  If we then plunged it into a bath at 100°K, it would solidify to $\ce{N_2O_4}$ and appear colorless.