How is the heat lost in a peltier distributed?
A Peltier device is not a marvellous means of heating unless you also value the ability to cool.

A Peltier cooler will transfer ALL electrical heat energy to the hot side PLUS any energy that is "extracted from" the cold side. So, if it is 5% efficient and you input 100 Watts of electrical energy you will get 5 Watts of cooling and 5 + 100 = 105 Watts of heating. While this is more efficient than using a resistive heater it is much more complex and costly per Watt than using resistive heating.