It is a fascinating subject, I have not been able to find useful internet data.
I built my first kilns over a winter. As i was burning off the dry wood I was taking beat up pallets to the dump, building kiln units, filling those with green wood. By the time spring came around I had my kilns all full of green wood with an Arduino and some temp and humidity probes in my home office. I had done one of the beginner kits with the LEDs and etc bits and "10 easy beginner projects."
By the time I got done with my spring chores, raking snow back from the edge of the roof, getting the rain barrels under the down spouts to catch melt water, all that kind of stuff - spray some chelated iron on the undersides of the raspberry leaves - my wood was already dry in the kilns. I still haven't hooked a temperature or humidity probe to a duino.
I have been thinking about this for years, but have no data.
One, get familiar with the EMC or equilibrium moisture content table. In general the hotter and drier your kiln is, the faster your wood will dry. +20 degrees F doubles the water carrying capacity (halves the RH) of the air inside your kiln.
Two, the fastest way to turn lumber into firewood is to put green lumber in a firewood kiln. We can do stuff - hot and fast- with firewood that would ruin lumber. We as firewood driers don't care about end checking or twist or discoloration, we just want it dry. As long as we get the water out of the tubules via capillary action before we really crank up the heat we are golden.
There is a guy at either Cal Tech or Cal Poly, an astrophysicist, who makes a hobby of taking close up pictures of ice crystals. His primary work thing is black holes or mesons or quarks or somesuch star trek thing, but he has a fascinating page of ice pictures - with a discussion of how water vapor moves around in air that is both sophisticated and accessible.
What i have found to be true in my kiln is what Mr.Dr. CalPolyTech calls window frost. You know when it is really cold outside and fairly warm indoors you get ice on the inside of the windows of your house? Because the windows are thinner than the walls the glass is colder than the drywall and water vapor in the air of your house condenses on the glass and actually freezes if the glass is cold enough. My kilns do the same thing. When it is really sunny out and the mass of the wood is heated through sometimes the temperature of my plastic cover is lower enough than the temperature of the air and wood inside the kin for water vapor inside the kiln to condense on the inside of the plastic cover, where it runs down the plastic and drips outside the kilns onto my lawn. No fan required. It is awesome, purely accidental. I had no idea it was even possible when I built mine.
If I do hook a fan up to mine I will start by having the fan kick on when the temp in the kiln was peaked and is starting back down, like someone already suggested. Let it heat up all day, get as hot and humid as possible, but as soon as the temp starts back down run the fan to pull all that hot wet air out and have another go at it tomorrow.
But before I got around to doing that my wood was dry. In general my kilns have a one inch gap, full perimeter around the base to let cool air in(and condensate drip out). At the top I have a hole about the size of a cantaloupe (maybe 30cm in diameter) for each cord of wood in the kilns. I like to have my green wood put up by Saint Patrick's Day (March 17) because usually I start seeing above freezing temperatures around April 1. By Summer Solstice (June 21) my wood for the coming winter is dry, about 14% MC usually. All I have left to do is keep it dry until the weather cools.
With a fan and some data I _might_ be able to shorten my drying time, but then I would have to pull all that wood out, restack it somewhere else, reload the kilns, dry a second load... With my current system I just order green wood when I have room in the kilns to stack it, and it is dry long before I need it.
I guess I would start by timing green wood drying from fresh felled to whatever your target moisture content is, running your kiln passive, just vented, no fan. You will likely need some way to quantify how sunny the weather is, not just the daily average weather temperature for your data to be useful across separate loads in the kiln. Once you know how many hours of sunshine it takes to dry freshly felled firewood to your target MC running passive, I personally would run the fan right after the temp has peaked in the kiln every day to see how much faster you can do it that way. I was going to point a solar panel at where the sun is in late afternoon and not even use a battery, just have the sun hit the solar panel late in the afternoon to run the fan until the sun moves all the way over the panel.
Good luck, looking forward to some more data.