Locating detailed average global rainfall and temperature data for use in QGIS

I’m looking for average/yearly global rainfall and average/yearly temperature data that can be synced up to terrain and elevation maps I currently have in QGIS. High accuracy is not crucial (any year, or even multi-year would be fine), but I want something a little better than the tiny maps I’ve found online. QGIS seems to like tif files but I’ve been unable to locate any with rainfall or temp.

I actually need these for a non-GIS related project (not scientific either), but it seems like I can use QGIS to ensure the maps are overlaid accurately, and to convert to greyscale values. (So if there are any large enough png or even jpg images which could be converted to greyscale, that would work too.)

Attached is an example (with elevation data) of what I want for the final product, scaled down drastically. The actual size is a 22,000 by 8,000 png with a transparent background (black would work too).

Edit – I’d also be willing to try and generate something using just numeric data, if it’s available anywhere…