How much warming there was over time for a specific month? I'm calculating warming trends in specific places and periods of time, that are related to the time a migratory bird spends in a stopover. But using different methods I got different results and I'm trying to figure out which is the most accurate. I know it will depend on location, so my sites are Southeast Canada and the Arctic. How much warming is possible in 40 years for example in a period covering only one month in spring, like May? What would be a good value to compare my results? spring temperature warming trend?

There's a lot of fluctuation in temperatures, so when averaging them I get no changes, including in the Arctic, which cannot be true. I looked at trends of the maximum temperatures and they are increasing, also investigated the anomalies, but I would like to have an advice.
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?