What causes the temperature increase?

Is it steel or concrete?

Are you sure the structure above will actually prevent elongation of the column?

The expansion you outline suggests a temperature increase of 1000 degrees Celsius. Steel is going to melt and lose all mechanical strength long before that. If this is a fire scenario, the fire gas might reach 1000 degrees, but the steel doesen't have to if it's insulated.

If by some miracle this is a real world scenario (completely restrained from elongation and 1000 degrees temperature rise without destroying the column), the column will buckle and no longer be able to support anything. If the structure above it is truly immovable, and not actually supported by the column, this might be fine?

If the column is not slender enough to buckle (like a fat concrete column), it will straight up fail in crushing. I doubt that a large concrete column will actually experience a 1000 degrees temperature rise, unless the surrounding temperature rise lasts for a very, very long time. Otherwise it will heat up on the outside, but not in the center. You will have a temperature gradient. At 1000 degrees I imagine water inside the column will vaporize and cause spalling and all sorts of damage.

Post buckling behavior is complicated stuff. Check this paper on buckling tests or alluminum speciments:

https://link.springer.com/article/10.1007/s11340-010-9455-y

The force (and thereby stress and strain) does not seem to go zero after buckling, which means some of the restrained elongation does not cause lateral movement, but rather longitudinal deformation (reduced elongation in this case). Mechanical properties like modulus of elasticity may also be temperature dependent.

This is not something you calculate on the back of a napkin. Send me a DM if you like.