The most important reanalysis datasets covering until present time (I'm excluding the others that stop some years before present time) currently available are:
- ERA5 by ECWMF: 1979-present (soon 1950-present), temporal resolution of 1 hour and spatial resolution quarter degree (0.25 x 0.25);
- CRU by the UEA: 1900-present (some variables 1850-present), temporal resolution 3 or 6h, spatial resolution half degree (0.5 x 0.5);
- GLDAS by NASA: 1948-present, temporal resolution 3 or 6h, spatial resolution quarter degree (0.25 x 0.25).
- ERA5-LAND by ECMWF: 1981-present, temporal resolution of 1 hour and spatial resolution 0.1°x0.1°, global coverage, but only land-covered surface.
(please, feel free to edit the answer to add more)
You could download one of those and process these temperature data using a simple resampling procedure bringing it at the resolution you are interested in by using CDO or another similar software. The procedure could be based on a bilinear interpolation of the original data with a finer grid. This would bring uncertainty because the correct procedure would be to use the reanalysis as boundary conditions in a regional climate model, but it would give a good approximation of the data you are looking for.
The only dataset I am aware of that is providing global data at a resolution of a 0.1 deg. resolution is the MSWEP by JRC and Princeton, but present data are not available for free, and it includes only precipitation data.