Maximum temperature possible on earth on a day
Maximum temperature over what area? There are of course local hot spots at hydrothermal and volcanic centers which far exceed the generally excepted maximum recorded temperature, of 58 deg C in Libya (as you correctly state). Many other high temperature anomalous areas exist in areas where there are no met sites to record them. For example, in the Afar triangle depression in the horn of Africa, or in the foothills of the Jebel Akhdar in Oman. In the latter case the steep slopes of black harzburgite rock re-radiates high summer insolation to well into the 50s, but as far as I know, the maximum temperature has never been investigated. Then there is the time-scale. Global warming will almost certainly increase the maximum recorded temperatures over the coming decades and centuries. 

On the geological time scale, the sun's radiance is very slowly increasing, so it is only a matter of time (billions of years) before the planet gets so hot that photosynthesis will cease - in which case whatever humanity evolves into will eventually fry.