Is CMB Polarization simply the temperature gradient of the CMB? Firstly, I have to admit that I don't fully comprehend the concept of "CMB Polarization". When I think of "Polarization", I normally think of the optical definition of polarization, as defined by the electric field. What I currently think is that CMB Polarization is simply the temperature gradient of the CMB. The Wikipedia page also said that:


  The cosmic microwave background is polarized at the level of a few microkelvin.


Since microkelvin is a unit of temperature, CMB Polarization must be somehow related to temperature. Is CMB Polarization simply the temperature gradient of the CMB?
Polarization of an electromagnetic wave refers to the extent to which the electric field (which is always perpendicular to the direction of wave motion) oscillates in one particular direction, rather than randomly in the plane perpendicular to the wave motion.

Complete linear polarization means the electric field oscillates to and fro along one particular axis.

Polarization of the CMB is produced by Thomson scattering from free electrons just before they combine with protons and the Universe becomes transparent to the CMB radiation.
The polarization occurs because the radiation field seen by the electrons is not uniform in space (not isotropic), it varies according to which direction the radiation is coming from. These anisotropies are the fingerprints of what went on in the early Universe and what the values of the cosmological parameters are.

There is an excellent primer on this topic - http://background.uchicago.edu/~whu/intermediate/polar.html

The CMB is a blackbody spectrum at a temperature of 2.7K. Differences in this temperature are seen on a variety of scales at levels of 30-60 microKelvin ($\mu K$). These are the "ripples" first seen by COBE, then WMAP and Planck with increasing precision and sensitivity to smaller angular scales.

Whereas expressing these spatial variations as differences in temperature seems straightforward, it is not so obvious why you would express polarization signals in the same terms.

In brief, what is going on here is that when a polarization signal is measured it is actually finding the difference between two perpendicular polarization intensities. Because these intensities are measured as changes of temperature in the bolometer arrays used as detectors, this is how the results of the polarization are expressed.

The polarization anisotropies are expected to be an order of magnitude smaller than the CMB temperature variations. That's because repeated scattering from free electrons can dilute the signal, so it is only light that has been scattered once that contributes.