I bought a little white Sunbeam plastic space heater at Wal-Mart for about $12. When I got it home, i held a thermometer up to it about 1" away, and the maximum temperature it reached was almost 120 degrees.
According to Wikipedia, cosmoline melts at 113-125 °F. So the heater is perfect for getting the wood to *just* the right temperature to melt cosmo.
I hold a small portion of the stock about 1" away from the heater, let the heat absorb into the wood, then wipe away the cosmo as it weeps. I continue the process and work on areas until the weeping stops. I keep the stock moving so there's no chance of scorching or overheating the wood.
This method worked excellently, and was very neat and clean. The only smell/fumes were the heater coil and the sweet smell of cosmoline.
Consider this: the cosmoline was applied to the firearm by heating up the cosmo to melting temperature, the item was slathered in it/dipped in it, and upon cooling the cosmo coated the item.
It seems to me the best way without chemicals to get cosmo out without harming the wood is to reverse the cosmo process, using what others have said too - heat. Use just enough heat to let the cosmo melt, wipe it off, and continue until all melted cosmo is gone. Whether this heat is in a black plastic bag on a hot day, near a fireplace, near a $12 cheap space heater, on a hot summer day out in the sun shooting the rifle...it doesn't matter. Let the heat get the cosmo out for you.
So my process:
Gather up plenty of rags you don't care about (Box o' rags, t-shirt cuttings, etc)
Plug in small heater, let it heat up on high.
Get a thermometer and confirm the distance you need the item to be, to subject it to about 115-120 degrees F.
Hold item in front of heater, watch for cosmo melting. Wipe with rags.
Work in small areas, continue until cosmo stops melting/weeping from stock.
Throw out rags.