I did not read all the answers, so maybe this is not interesting or new: But I just want to tell you the best way IMO
Heat the soup (!) and heat it as high as your solvent starts to boil.
Then throw your pulling solvent into the soup.
Indeed mixing both will equilibrate the temperature inbetween, but there is 1 important thing:
Your pulling solvent will definetly have a lower Heat Capacity (than the water aka the soup) - meaning that it gets warmed up much faster in comparison to water.
This means FOR EXAMPLE
1 L Water (60 °C) + 1 L Hexane (20 °C) will not be at 40 °C, but somewhere 50 - 60 °C.
But if you just heat your soup to the vaporisation temp of the pulling solvent, then you will not come out on a higher temp, so you dont have to fear that it will instantly start vaporizing like hell upon combining.
Ok so this for the pre-heating ...
Then I would advise to slowly heat up until you actually reach that evaporation temp of the solvent and try to let it stay at this point or just below it.
If you plan on letting it stirr together for a long time like 5 minutes or even 10, then you should stay some degrees below that vaporisation temp however.
And for that question: Heat it at all, or not heat it at all -> I would say ALWAYS heat it and ALWAYS heat it to the maximum of your solvent.
You should recrystallize it after you're done anyways, so that little more impurities are totally not bad, as you will get rid of them anyways.
Don't worry: *Recrystallizing* seems to be another thing on top of your route and you may think "ugh ... do I really have to make even more efforts?"
But it is really fast, you will see and so easy. People say: You will loose some of your product. But in my opinion you simply loose the impurities, therefore of course it gets lighter. But it is always worth it! Just make sure that you freeze-precip it fully, then you wont loose any noticable amount of your actives. Plus even when *not focussing on purity* by heating while pulling, after the recrystallization your product will still be like 95 % pure or higher, easily, if done right. Therefore its no real choice between purity and yield.
Let's take a look why I would highly advise it doing it that way (numbers are just examples):
A.) No Heating: You will need 6 pulls to get everything out, which could be 6 x 100 = 600 ml
B.) Heating at max: You will need 3 pulls to get everything out, which could be 3 x 100 = 300 ml
Then you will recrystallize afterwards anyways. You will need lets say 100 ml.
A.) = 6 x 100 + 100 = 700 ml
B.) = 3 x 100 + 100 = 400 ml
Just a rough example, but it is like this. Also you dont know if room temperature will EVER get even the last bit out, maybe even the 6th pull is missing some little amount.