Where can I find daily minimum / maximum temperature for Africa, possibly in a raster format?
A data requirement like the one you have outlined requires either a series geostationary satellites, or modeled data based on an amalgamation of data sources.
Geostationary satellite: Your best bet would be the Meteosat MSGs. Working with this data is not the easiest task in the world, and accessing data is not easy either. For research projects, this data is usually free, but for commercial projects it becomes expensive.
Modeled data: Personally, I'd suggest GLDAS data products, particularly a combination of NOAH versions 1 & 2, to cover your time period. The data is available in 3-hour timesteps at 0.25-degree resolution. Data is in GRB-format, but new versions of ArcGIS can read this data as a raster.
Check this site http://www.worldclim.org/. The raster resolution is ~1km (30 arc-seconds).