As far as finding the global mean temperature for a given day,  the source to consult is NASA's Goddard Institute for Space Studies' Surface Temperature Analysis or "GIS Temp."  Since NOAA's "State of the Climate" measures the global mean temp every month--and publishes the finding in the middle of the next month--GIS Temp must be monitoring the relevant data more or less around the clock around the world. 

"The GISS Surface Temperature Analysis (GISTEMP) is an estimate of global surface temperature change. Graphs and tables are updated around the middle of every month using current data files from NOAA GHCN v3 (meteorological stations), ERSST v5 (ocean areas), and SCAR (Antarctic stations), combined as described in our December 2010 publication (Hansen et al. 2010). These updated files incorporate reports for the previous month and also late reports and corrections for earlier months."

https://data.giss.nasa.gov/gistemp/