Sun synchronous satellites like Landsat always capture an image at the same time of the day. Furthermore, Landsat "only" repeats its acquisitions every 16 days.
If you want an image in the afternoon, MODIS AQUA has a daily coverage at 1.30 PM, which is a better timing but at a lower spatial resolution (500m).
Finally, you can get the highest temporal resolution with geostationnary satellites like METEOSAT-5 MVIRI, but then you have a spatial resolution of 5 km.
As you can see, the best spatial and temporal resolutions never come together.
As a last remark, land surface temperature is not a direct measurement of the temperature of the air but depends on the emissivity of the observed land cover. This has to be taken into account for some applications.