You mean 'sodium carbonate'. I know yu are abbreviating for simplicity but with chemistry and when asking for help/advice, its good to be exact, because a small mistake can make worlds of difference (for example if you use another carbonate and not sodium carbonate).
As for the losing yield during wash, you're right the DMT should not move to the water if the pH is high enough. A side by side with a quick vs long wash could answer this once and for all.
Regarding pulls, its hard to say because there are many variables appart from temperature. Unless you mix with a magnetic stirrer in the exact same amount of time, there will be other variables involved because you may mix more or less depending on the pull, etc. But I can say that, from experience after many extractions, first pulls tend to be whiter, later pulls tend to be yellower, heated pulls tend to be yellower, long-standing pulls tend to be yellower.
Heating pulls can be done to the solvent, or to the whole mix (please do it safely, FAQ has instructions). Its true that the whole thing will cool down if you mix warm solvent, but if its really warm, it may take a few seconds to cool down which could be enough to increase solubility and increase yields, and once it cools down the DMT wont move away from the naphtha, it will stay in it, and the naphtha will be saturated. Yu can mix the whole thing too, though, thats maybe overall more effective? You could do a side by side and let us know

I disagree with kash, washing is not useless, and defat is a wasteful unnecessary process IMO. Check the FAQ regarding if you should wash the spice. If you do a re-x, indeed a defat is not necessary, though, because the lye traces will go to the bottom goo which you decant the solvent from.
And regarding defatting, if you get yellow, you can easily recrystallize your product with minimal amount of solvent, instead of wasting tons of solvent for defat.