The parents alone will eat the babies. I had a tank with 8 females and 2 males. They had so many babies, but the population of the tank was kept in check because the other fish ate so many babies that only 4 made it to adult size.
Guppy's breed very easily in captivity. Once they mate, the female can save the males sperm in her body for up to 8 live births. So you can imagine how it can get out of control if every baby survives.
You have a few options....
First, when the babies are born they instinctively swim to the bottom of the tank and look for hiding spots where they will have a better chance of avoiding other fish. You can add more low cover plants or tightly packed rocks for more hiding spots which will lead to better chance of survival.
Or, you can buy a breeding container where you put the pregnant guppy in and leave it their until it gives birth. The container has a small slot that the baby swims through but the mother cant fit. A cheep breeder will only set you back 5 bucks or so. The container sits in the tank.
If you want to keep the babies in your other tank you mentioned just get a heater.
But i promise you will have lots of guppy's in a short time if you keep every baby.
Someone else might have a better answer but that's my experience with guppy's.