I've never heard of putting a "poolish" into a refrigerator. Perhaps the best known poolish formulations on this site is Jerry Mac's NY Style Pizza. Instructions below:
Water (68%) at 68 degrees
Thickness factor = 0.096738, bowl residue compensation is 2.6%.
Combine yeast and flour. To create the preferment “poolish” take 2/3 of the flour/IDY mix and ALL the water and wisk together. Use a Danish dough wisk or paddle attachment on mixer.
Cover mixer bowl and preferment for 5 hours at a room temperature of about 67 degrees F. Note that the poolish can be used a reasonable period of time after the poolish reaches the "break point". The break point is the point at which the poolish peaks and starts to recede, or collapse. All else being equal, the time that it takes to reach the break point will depend on the temperature at which the poolish preferments. Higher temperature = less fermenting time.
After the preferment time add the honey, salt and the remaining flour/IDY mixture to the poolish in the mixer bowl. Use the C-hook to mix at stir speed.
Once all of the ingredients are fully combined, knead or about another 3 1/2 minutes at speed 2.
Remove dough from mixer bowl and place on a lightly floured work surface, hand kneaded for about a minute, and shape into a round ball. Put the dough into a covered oiled container and ferment for 1 ˝ hours.
At the end of that time, punch down the dough, reshape into a ball and proof for another 1 ˝ hours (also in the covered storage container).