Newton's Law of cooling has the following formula:
T (t) = T_e + (T_0 − T_e )*e^ (- kt)
where T (t) is the temperature of the object at time t, T_e is the constant temperature of the environment, T_0 is the initial temperature of the object, and k is a constant that depends on the material properties of the object.
So, k is a constant in relation to the same type of object. If we change the object and its material properties, the constant k will have a different value (for instance, silver will have a different k from wood).