What would the method be, though?
Same as any calorimetry method except use some liquid that will not react with water (and of course one for which you know the specific heat).
Can you exlain more on your answer, I am not quite grasping what you are saying.
How do you determine the specific heat of a metal. You heat it to a specified temperature, transfer it to water at a known T and measure the rise in T of the water. Could you enclose the Na metal in a non-reactive metal container (one which you have already measured the mass and specific heat), then heat the whole thing up, place it in the water bath, and measure the rise in T of the surrounding water. This isn't quite what I had in mind when I first asnwered but check my thinking on this.