Does the reaction become more or less favorable as temperature increases?
You should use the van't Hoff equation together with the standard enthalpy of reaction $\Delta H^\circ$ for the process to predict the response to a temperature change. This should provide you with a prediction consistent with Le Châtelier's principle that an endothermic reaction is pushed in the direction of products as $T$ increases.

The general equation for the Gibbs' free energy $$\Delta G = \Delta H - T \Delta S$$ should not be relied upon to determine the response of the reaction equilibrium constant to $T$. The expression is valid at constant $T$, but this is not the problem with using this equation, rather it is its generality: it is not limited to describing reactions at equilibrium. Note that $\Delta G = 0$ for a reaction at equilibrium. 

On the other hand, you could consider using $$\Delta G^\circ = \Delta H^\circ - T \Delta S^\circ$$to guide you, and the result should be consistent with analysis based on the van't Hoff equation. It is simpler however to work with the van't Hoff equation directly.  In fact, assuming $\Delta H^\circ$ and $\Delta S^\circ$ are independent of $T$ you can use fairly straightforward mathematical manipulations to arrive at the usual integrated form of the van't Hoff equation.