The only way you'll keep the temperature level is by attaching the heating device to a thermostat. This isn't ideal with a bulb as it means the light will keep going on and off. Better to use a heat mat.
Definitely take them away from mom - as well a normal tank as not being humid enough, she doesn't care about the eggs and she might knock their container. If snake eggs are turned, they often die.
Cheers
Kel