It does make a big difference. Naphtha doesn't hold much DMT at room temp. If you heat both the soup and naphtha up to 140f / 60c, and pull with small amounts of naphtha, you'll ensure every pull is saturated. The big crash of crystals in the freezer is worth it IMO. Heat is correlated with shifting the color yellow, though.
But yes you could do it at room temperature and it will still work, just use small amounts of naphtha to ensure the pulls are saturated. If you use too much naphtha and nothing freeze precipitates, evaporate half of it away and try freezing again.