How does Lightroom and PS guess color temperature?

The basic answer is "it depends" on what settings are selected in LR/PS (Lightroom/Photoshop).

Most of the time it is based on in-camera processes that set the color channel multipliers in the EXIF info but raw conversion applications, including LR and PS that both use ACR (Adobe Camera Raw) under the hood, can be set to use other things instead. That can be as varied as letting ACR apply its own "Auto WB" computations to using a manually selected WB (White Balance) using the Adobe application to a saved "Custom WB" created using the Adobe application(s).

How each camera does it can vary significantly from one model to the next. Even with the same camera, WB settings can be altered. Results will be different between 'Auto', a 'Preset' such as "cloudy" or "fluorescent", manually set WB, or a custom WB. Even when WB is set manually, the camera usually still does an assessment of the captured image data and saves the "automatic WB" computation in the EXIF info as well as the manually selected WB that is applied to the JPEG preview image.

There's also no guarantee that ACR/LR/PS will recognize the in-camera WB settings and use them. Particularly with "Picture Styles" (Canon), "Picture Controls" (Nikon), or any other similar name used by other camera makers, Adobe will often ignore them. Ditto with Custom White Balance set in the camera.

Please also see this rather extensive answer to What *exactly* is white balance?