Assuming you don't have anything boiling or frozen, the water temps will just average out, right?
I'm still a wort-virgin (for a few more hours anyway) but my idea is to chill the top-off water as much as possible during the other work. The colder the better, just as long as it doesn't freeze.
If you're an engineer type like me then -> When you're ready to top off, take your pitching temp and muliply by 5. Take the temp of your top off water and multiply by two. Subtract the 2nd number from the first. Divide the result by 3. That's the temp you need to cool your wort to.
If your pitching temp is 70, a good target would be 75.
Assuming your your top off water is cooled to 40degF..
5 * 75 = 375
40*2 = 80
375 - 80 = 295
320 / 3=98
So 3gal at 98 + 2 gal at 40 = 5 gal at 75..
Once the full batch of wort is at 75, it shouldn't take much longer to hit 70..
Anything wrong with this?