When current is injected into a Peltier device/thermo-electric cooler, it heats up, when the current is reversed, it cools down. Why does it takes less time to heat up than to cool down?
Peltier devices are quite inefficient. A simple first-order approximation for a Peltier is a perfect heat pump in series with a resistor. The heat pump moves heat symmetrically proportional to the current, but the resistor always makes heat proportional to the square of the current.
The unavoidable heater in a Peltier device makes it overall better at making heat than cold.