For the reaction: $2{\mathrm{NO}}_2\left(g\right)⟶{\mathrm{N}}_2{\mathrm{O}}_4\left(g\right);\mathrm{\Delta }H<0$. 

What predictions can be made about the sign of $\mathrm{\Delta }S$ and the temperature conditions under which the reaction would be spontaneous?

Given reaction is,

$2{\mathrm{NO}}_2\left(g\right)⟶{\mathrm{N}}_2{\mathrm{O}}_4\left(g\right);\mathrm{\Delta }H<0$

Here, enthalpy is positive. When the temperature is increases, the change in entropy also increased.

Thus, $\mathrm{\Delta }{S}_{rxn}$ is positive at high temperature.