4 Pelteir Plate Water Bottle wired to Arduino Uno
When it comes for amount of power from laptop, then this is not realy reasonable to expect even USB3, maybe some older laptops PCMCIA, or hardware docks. When it comes to Desk, They would have to be adjusted to get the ATX from PSU (it would have to be upgraded for purpose) We are still talking about a small Can or Yacult botle...
Even then insulate, insulate (and same again) 
Then its a question of speed and how hot or cold) Battery pack that charges even when not used, used as buffer might work (for a short time).Controlling it from Arduino is easy part using function that switches one on other off whenever you want and then calling the function itself to make sure both steps happen, rather then manualy editing or using one output for controlling power on/off and another on two way relay switching between sets (relay would increase consumption here).