How much warming there was over time for a specific month?
It is hard  to help unless you clarify what methods have you tried. However, I would suggest to explore reanalysis weather models, as they are the most accurate source of estimated weather conditions worldwide in the past.

A recommended reanalysis is ERA-interim, starting in 1979 so it gives you  39 years, if you really need 40 you can use JRA-55 that starts on 1955.

The KNMI Climate Explorer is a great way to retrieve and plot data from those models.

If you get in there you can set it to plot monthly mean temperatures for a given location. Here is an example of somewhere in SW Canada:


That will produce a plot like this:


Were you can click the "raw data" to get the raw values, and that will produce an output like this:



Where each row is a year and each column is a month. So you can pick the column of the month of your interest and compute the trend from that.

Does it makes sense?