You can't blow cold air in without blowing warm air out.

And definately measurable, unless you go way, way bigger.

(I didn't verify the numbers)

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You can pump the heat into the ground water or something. It still would have to dissipate somewhere. So if that ground water feeds into some river 5 days downstream, it would show up there. Maybe not after 5 days as it seeps through huge amounts of ground rock but weeks later or so ... you would have a signature if you had the prior temperature.