The energy it takes to heat water is in kWh, not kW/h. If we're talking about actual desalinization through evaporation, don't forget the energy cost of the phase change, which is what takes most of the energy- just boiling ten liters of water already at 100 c takes another 6.27 kWh. So with the .937 you mentioned for heating from 20c to 100c, 7.21 kWh overall. Or in cubic meters of water, 721 kWh/m^3.

But actual desalinization plants recapture almost all of that energy to heat the incoming water, so the effective energy used is far less than that. According to this it's around 10–16 kWh/m^3 for multi-stage flash distillation, which is the efficient form of the evaporation process we're talking about here. But reverse osmosis is even less, at 3-4.

Description of multi-stage flash distillation from that link pasted below, because I found it interesting:

Saline water blended with recycled brine, preheated within the middle stages, is brought to working temperature (usually between 90–110 °C) with steam, in the Heat Input Section. At this point, it is transferred to the first stage, which is kept at a lower pressure than the heated saline water equilibrium pressure. Consequently, the saline water becomes partially vaporized. Steam generation removes energy from the mass of saline water, therefore cooling it to a certain extent. Furthermore, steam extraction results in higher salinity and higher boiling point in the case of the remaining saline water. The steam is transmitted to demisters, where transported droplets are eliminated, then it flows into a heat exchanger at the top of the stage. Consequently, the heat of the steam is passed over to the incoming saline water, whereby the steam cools down and condenses. By this process, the heat can be recovered with high efficiency.