1. Eigenvalue Buckling is a solution to determine the critical load when buckling occurs and the shape it would take after buckling. It is not to determine the amplitude of the buckling. Use a nonlinear (large deflection) Static Sructural analysis to determine the deformation post-buckling.

2. A negative load multiplier means that there is a buckling solution in the other direction from the applied load. If the load was a compression force, that means the struture could buckle in tension.  For temperature if the load was to increase the temperature, that means the structure could buckle when it gets cooler.  Sometimes these mathematical solutions make sense, and sometimes they don't.

3. When you created a Fixed Support, at one end, what was the new load multipliers? You have to recalculate the temperature if they changed.  Also, try applying the temperature load of 23.4 C (or whatever the new number is) and see if the Load Multiplier comes out close to 1.0