How do we do data binning in statistical analysis? Is there any standard for binning temperature data?

There are no standards, but there are some commonly used methods. One class would be to decrease resolution to five or ten degree intervals (say for weather measurements). Of course, you are already doing that with you original measurements which are probably started to 1 degree or 0.1 degree resolution which is effectively a way of binning. Obviously, this depends on the measurement as well. 10 degree bins would make no sense for plasma physics, for instance.

A more universal approach would be to bin into quantile ranges such as deciles or quintiles based on previous observations. This won’t be as user friendly because the ranges won’t have pretty boundaries.