For cooling the printed object:
- Combined with air compresser
What seems the most practical is to use an air compressor with a tank large enough to ensure that the air in the tank has time to cool off. This gives you the option of adding an air dryer if needed. You could cool the compressed air just before blowing on the print though a Peltier cooler and get additional cooling as the air releases toward the print.
- Printer Ceiling
You could put a Peltier cooler on the ceiling with a heatsink/cold-sink covering most of the inside ceiling and fans only on the external (outside the ceiling wall) heated part of the Peltier. Convection would move the air. Without and enclosure, positioning the Peltier to use convection would be good because the fans, especially those removing the heat would not be fighting convection.
- Printer Bed
You could use a Peltier cooler to both heat and cool the print bed. All you need for stitching is to change the polarity of the voltage on the Peltier. A Peltier could handle those temperatures well. While Peltier heaters/coolers aren't energy efficient, because they can do both, they have good and quick temperature control.
If you wanted to get fancy, you could have multiple Peltier devices across the bed, so that you could keep heat under the print and have all the other devices cool. You would need to know the fastest rate you could change temperature without cracking the glass on a glass bed.
Cooling the heat sink on the extruder. (answering a different question)
The most practical way to use a Peltier cooler is to take advantage of its temperature differential over a short distance. One could put it between the heater block and the heat sink, requiring a hole in the cooler for the filament to feed through. The Peltier effect has a limit of a 70°C maximum differential between the hot and cold side. Another limit is manufactures list a maximum temperature of 200°C on the hot side. This is usually because of solder joints.
The Peltier cooler would need to be customer made to fit between the heater block and heat sink a) hole in the middle, b) designed to withstand heater block temperatures >200°C.
The heat sink probably still needs a fan due to the maximum temperature differential of 70°C. A 70°C maximum temperature differential makes it difficult to be the only source of cooling. Rarely are Peltier coolers the only source of cooling. Only when they are in an insulated barrier such as in the wall of a ice chest. Other wise the heat from the hot side mixes with the cold side. Peltier coolers move heat from one surface of the material a short distance to the other side of the material. If you don't cool the hot side of the material, when using it in an open area such as an extruder, the heat will circle back around to the cold side.
Its main advantage would be a fast drop in temperature between the heater block and heat sink. However, it is an expensive project, and one needs to evaluate of this could be better achieved by other methods.
Links using Peltier cooling with 3D printers: