What does geochemical data tell us about Earth's earliest palaeoclimatic conditions?
The first thing to note here is that the zircons you mention in your question are the only thing we have dating from the Hadean: no known Hadean continental or oceanic crust have been found to date. So, all informations come from these zircons.

What do they tell us? 

The rare earth element (REE) composition of these zircons (and in particular the zoning of said REE inside the mineral) suggests that they formed in a magma derived from the melting of a continental crust (Wilde et al. 2001). Their high $\delta^{18}\mathrm{O}$ composition also indicates that the magma was at some point in contact with liquid water (also Wilde et al. 2001): both continents and oceans were present in the Hadean. The presence of liquid water already implies cooler temperature than what was previously thought (Valley et al. 2002).

With regards to climate per say, the Lithium composition (high concentration, light isotopes) of the zircons (Ushikobo et al. 2008) have been interpreted as evidence of an intense chemical continental weathering. This weathering could have several explanations but one possibility retained by Ushikobo et al. 2008 (see also Sleep 2010) is a CO2-rich atmosphere with surface temperatures above 50°C.


Sleep, 2010. The Hadean-Archaean Environment. Cold Spring Harbor Perspectives in Biology, 2: a002527.
Ushikobo, Kita, Cavosie, Wilde, Rudnick &amp; Valley, 2008. Lithium in Jack Hills zircons: Evidence for extensive weathering of Earth's earliest crust. Earth and Planetary Science Letters, 272: 666-676.
Valley, Peck, King &amp; Wilde, 2002. A cool early Earth. Geology, 30: 351-354.
Wilde, Valley, Peck &amp; Graham, 2001. Evidence from detrital zircons for the
existence of continental crust and oceans on the Earth 4.4 Gyr ago. Nature, 409: 175-178.