In a previous paper (Chassefière et al. 2013), we have shown that most volcanic sulfur released to the early Mars atmosphere could have been trapped in the upper cryosphere under the form of CO₂-SO₂ clathrates. Huge amounts of sulfur, up to the equivalent of an ~1 bar atmosphere of SO₂, would have been stored in the Noachian upper cryosphere, then massively released to the atmosphere during the Hesperian due to rapidly decreasing CO₂ pressure. It could have resulted in the formation of the large sulfate deposits observed mainly in Hesperian terrains, whereas no or little sulfates are found at the Noachian. In the present paper, we first clarify some aspects of our previous work. We discuss the possibility of a smaller cooling effect of sulfur particles, or even of a net warming effect. We point out the fact that CO₂-SO₂ clathrates formed through a progressive enrichment of a pre-existing reservoir of CO₂ clathrates and discuss processes potentially involved in the slow formation of a SO₂-rich upper cryosphere. We show that episodes of sudden destabilization at the Hesperian may generate 1000 ppmv of SO₂ in the atmosphere and contribute to maintaining the surface temperature above the water freezing point.