I need an explanation and example of the iso 17025 measurement uncertainty
pricipal. Ideally, include a numerical example. I need this in relation to
the calibration of a honeywell udc3000 temperature (type K) controller
with a unimat mcx calibrator. Example should show all the factors
included in determining the uncertainty.

I suggest you look at the examples provided in the document EA-04/2
"Expressions of the Uncertainty of Measurements in Calibration"
(http://www.european-accreditation.org/pdf/EA-4-02ny.pdf) which is the
guidance document for 17025 accredited laboratories of the European
accreditation bodies.
You may also want to consult the following document:
http://physics.nist.gov/Document/tn1297.pdf