One of the Nunc publications has elaborate and detailed suggestions to decrease rate of evaporation during cell culture. The cells you are culturing definitely at very high temperature, I am not very sure whether following the suggestions available through Nunc will help you or not but at least these are good to know.
1. Use an optimally performing humidity control.
2. Limit the number of outside inspections.
3. Keep the outdoor periods as short as possible.
4. Take the plates the shortest possible distance from the incubator.
5. Move the plates slowly.
6. Do not open the incubator unnecessarily.
7. If possible, add water or medium to the spaces between the wells.
8. Use larger volumes of medium in corner wells, or in all peripheral wells.
9. Use greater depths of medium in the plates which have a high evaporation index
Points 7-9 seems more logical and could be easily applicable to serve your purpose.
Interesting question. It strongly depends on the circumstances whether you will be able to control them. What is the vessel for your cell culture?
Petri disk: no way to avoid evaporation
Single well in a 96 well plate: good, if you fill the neighbouring wells (all 8 of them) with an excess (>5 times the volume of your well of interest) of the culture medium of your cells of interest, and leave the rest of the plate empty.
It is a simple matter of thermodynamics ;) Small droplets tend to evaporate to large ones, so you have to provide more large droplets which will do the battling between them and leave the small droplet unaffected. No formulas needed, works.
If you are incubating archaeal cells in petridishes, then it is better to keep the plates in a box and provide a glass/cup filled with water. We usually do this when incubating the cells for longer durations. And, to provide aeration, the lid of the box is slightly opened (in my case, i use papertowels to lift the lid of the box).
If not incubating in petridishes, then i dont know how :/