How to get an Intermediate value ?

It looks like you had a good ideas of how to solve it! A possible function to use is TREND. In this case, the dependent variable is the Density and the independent variable (the one you can alter) is the temperature. Excel expresses the independent variable as known Ys and the independent variable as known Xs. The value you want to solve for is the new X (or Xs). If your new X value (57 C) is in cell D4, the formula is

=TREND(B4:B18,A4:A18,D4)

giving an anwser of 1.072117 - somewhere between the values of 50C and 60C as expected. This is only an approximation as it is using a least squares fit. The result for 50C and 60C are slightly different from the 'observation'.
TREND can be used as an array formula.
Hope this helps.