Plotting distribution of a variable on the map with a shape file

[fyec]

I have a shape file of the region and values of the monthly mean temperatures of the locations over the years.
I want to plot monthly temperature distribution on the map according to each location's value together with the shape file that shows edges of the region.

For example, I have these data with 0.25 degree resoultion.


I want to plot this kind of distribution figure:


How can I start to plot this figure?
Thank you for your help.