Unfortunately, you can't measure BTU's, at least not directly in the field. Theoretically, it could be done by tracking gallons per minute and temperature differentials of chilled water through the air conditioners, if you have that type of system, but that's pretty impractical and hardly worth the equipment it would require.
For data equipment, BTU's are directly related to power consumption, so if your hardware is all on UPS, you can get a pretty good idea by taking UPS readings and multiplying by 3,400 BTU per kilowatt. However, this doesn't include the cooling required for sun loads on the building (hopefully you don't have Windows), outside air entering the data center (known as infiltration), humidification, and a number of other factors.
If you could give us a better idea of how you think tracking BTU's would help you, and what you're looking to do with the results, perhaps we can suggest something that would help you achieve your goal.
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