For any chemical reaction, Equilibrium constant is dependent on temperature. Any reaction will always have the same value of Equilibrium constant if the temperature at which reaction is carried out is kept same.

Therefore, Equilibrium constant at constant temperature is a characteristic property of a reaction i.e. it will always be same if temperature is same.

Equilibrium constant is not independent of temperature.

For e.g. consider an endothermic reaction. The reactant will require heat in order to proceed in forward direction and form products. So, if the temperature is increased, reactants will get heat to carry out reaction and more product will be formed at higher temperature. Thus, Equilibrium constant (which is basically the ratio of concentration of product upon that of reactant) will increase.

Therefore, we can say for endothermic reaction, increased temperature will be favoured and more product will be formed which in turn will increase value of K.

And for exothermic reaction, reverse is true.

So from this it can be said that K is dependent on temperature.