For example you putt those pieces like 24 hours (depends on thickness) before measuring in that room, the piece should have from it's core to the edges the same temperature.

Airflow inhibits a precise measurement, imagine you putt something in that room that changes the airflow just a bit, so more warm air from the ceiling hit's one side of the piece.

Always when you try to measure something, no outer energies should interfere (no temperature change and no force like airflow or even driving cars outside of the building), it could even be, that the airflow creates vibrations in the piece, like rolling cars do.

The issue is that the temperature in the room is non-uniform. The ceiling is 20 degrees hotter than the ground so over time the object will have the same distribution.

without HVAC wouldn't the temperature already change drastically throughout the day due to weather?