When an object gains heat it tenslds to expand, and when heat if lost it tends to contract. If the rate of expansion of the bubble is less than the expansion of the fluid the bubble will get smaller, and if the rate of contraction of the bubble is smaller than the rate of contraction of the fluid then the bubble will get larger.
As to the accuracy of the level, that should remain unaffected as the level itself operates by the relative density which should remain unchanged.
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