If you assume that they don´t react with each other in aqueuos solution means there will not be any reaction when they are in water. If you change the temperature will not make any change.
In the other hand, the change of the temperature does affect the the reaction ,the bicarbonate ions must come into contact with the hydrogen ions in just the right way. The probability of the bicarbonate and hydrogen ions doing this is affected by temperature: the higher the temperature, the faster the molecules move; the lower the temperature, the slower they move. But this is normally in aqueous solution.
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