Given that if mechanical energy is converted to thermal energy, then the spring would not compress as far as it would otherwise. This will cause the spring constant to be lower than it really is.
This statement is false. Because if mechanical energy is converted to thermal energy, there will be distortions in the solid pattern of the spring. And this will make the spring to compress.
Also, no matter what may happen to the spring, the spring constant remains constant. That is, unchanged.