Time to warm a volume of air to room temperature in a container

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RecoveringMoron
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Positing an empty container, underground, with a static temperature of 50F (both container, earth, and air temperature) and a volume of X...

and introducing (and displacing) into this container a parcel of 30F air of volume Y (which is less than the volume of X)...

Is there any way to determine how much time it would take the 30F degree air Y to warm to 50F?

Thanks much. Just trying to think about if buried air tubes to collect mean Earth temperature might be useful for a project. Thanks much for any help.
 
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Google earth tubes for much good information. There is a lot of experience out there with them.