For me the confusing part is the "raise naturally" part. How fast and how high it raises naturally would be greatly effected by the ambient temp at which you store your fermenter.
You are right.....I should have made this detail clearer, as it is extremely important, and a bit complicated.
To start, if you are relying on ambient temperature, you are going to be, ahem, urinating into the wind. To be clear, if you have to rely on ambient temps, throw out the fermentation schedule, and just pray for the stars to align. You still have a shot at making great beer, many do, but the fermentation is largely out of your control, and the results will be inconsistant as the seasons change. That is a fact. If you are in this position, pitch into the primary, try to keep it from getting too hot, and hope for the best. Rack from primary 4 weeks after you pitch. And drink. There, that is settled.
If you want to have the best fermentations possible, on our scale anyway, the only way you can really run an accurate fermentation timeline is if you can dial in an exact temp digitally, using some combination of an element for cooling the ambient air (like a cold basement/garage or converted fridge/SOFC - and to be clear, you will need ambient temps to be at least 10 degrees F colder than your desired fermentation temp) and an element for heating the carboy itself (like a brewbelt or fermwrap). A thermowell stopper or carboy cap thermowell will not hurt, but taping and insulating your probe againt the side of the carboy still gives you an accurate reading. Obviously, a digital temperature controller will also be needed. If you (like me) only have a one stage controller, you will need to use it on the heating element, and you will be cycling the heater more often to offset the larger gap between ambient. If you have a two stage controller, and some type of chamber, you would be using it on both the heating element and the chamber, and you can keep that temperature gap a little narrower.
To illustrate, if I was brewing an American Pale Ale this weekend with WLP001, my fermentation schedule would be as follows.
Saturday morning- make an appropriate sized starter with 1.040 wort and a vial of WLP001 or pack of WY1056. Get it on a stirplate at room temperature.
Sunday morning - start brewing.
Drink, eat.
Sunday afternoon - stop brewing.
Cool wort in kettle and move to carboy. Oxygenate. Put carboy in my fermentation chamber (minifridge) and set up fermwrap, thermowell, and digital controller. For WLP001, I would set the controller to 63F with a 1 degree allowance (for WLP007, my other favorite ale yeast, I would set this temperature, and each one to follow, one degree colder). This time of year in NJ, the immersion chiller seems to have the wort ending up around 60-62F, so there is not much waiting time before pitching, but I will emphasize the need to wait until the controller reads 63/62F before pitching my starter on Sunday night. No, do not pitch warm! In the winter I might have to wait an hour or two for the wort to heat up, in the summer it might take an hour or two for the wort to cool down. Either way, I am pitching on Sunday night when the controller reads 63/62.
Monday morning (about 12 hours after pitching) I increase the temperature on the controller to 65F. In my eyes, this is a neccessary step we have to take to emulate the "naturally rising" temperature schedule that huge breweries use. They have the advantage of experience that comes from thousands of fermentation cycles, so they know their yeast, and how quickly their temperatures swing. We have no where near that experience, so I think it is important that we coax the yeast along through the cycle. I leave the yeast at 65/64 for the next 24 hours.
Tuesday morning (now 36 hours after pitching) I change the controller to 68 degrees. This setting will allow a maximum temperature of 68, but in reality, since the heater kicks off when the probe in the thermowell measures 68, the temperature is most often at 67F. When it briefly drops to 66, the heater fires until it hits 68, then again, slowly drops back to 66. I would say that 90% of the time, it reads 67, so don't think that the temperature is all over the place. I leave it set at 68 for the remainder of fermentation. If you want to rush things, you can crank it to 72/71 for a D-rest after a week or so, and then crash cool to clear the beer, enabling you to bottle within 2 weeks of brewing. Fermentation will certainly be over, but you just took away the beer's chance to condition. It should be obvious, but I no longer support that practice. I tried it for a while, but my experiences with both options have led me back to just "leave it be" at 68 for 3-4 weeks; whichever is the more convenient weekend for me to rack and bottle.
As an aside, if the recipe calls for a dry hop, I do it right in the primary, no hop bag, one week before I plan to bottle. No need to crash or raise temperatures for the dry hop. No need to move to secondary. Just leave it be, and the hops will settle to the bottom before you will need to rack. I can't speak for oak or fruit, but if I had a gun to my head, I would just toss those into the "primary" as well.
Can you still call it a primary if there is no secondary? Would't it just be a "carboy" at that point?
Hope that was clearer than the earlier answers. I hate when a question is left hanging.
Joe