I'm now curious. If there is a deep secret facility somewhere, how long does it take for heat to dissipate through the rock. Let's say you dig 500m deep and through some layer of ground water that you use to cool down any air from ventilation to ambient temperature. Let's say it's a 10MW facility. Unless there is good data on the temperature of a wide area prior to the installation, you wouldn't notice this as the heat would dissipate over a wide area and even 10MW would not make a dent compared to what the sun radiates on a square km for example.
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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)
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.