Hi Zoe it would be useful if you could explain a bit more about the application.
You can power the Uno from the battery (as has been said ) by connecting it to the Vin and ground, or with a suitable connector to the barrel jack.
However
which peltier / ptc? (type number, link to daya sheet)
Specifications:
Suitable Semiconductor Chilling Plate: TEC1-12706
Material: Metal
Voltage: 12V
Electricity Current: 5.8A
Power: Qcmax 50-60W
Weight: 350g
Fan size: 92 x 92 x 25mm
PTC
Product Specifications:
Constant temperature: 80/120/220 degrees
Input voltage: 220V/12V/
Max power: 30W
Size: Appx.35 x 20 x 5mm
Wire length: Appx.140mm
Heat material: PTC Thermistor
Heat methods: heat conduction
Lead wire: high temperature line
Package include : 1 Pc x PTC heating element
The temperature of the product identification refers to the ambient temperature of 24 degrees, the maximum temperature of the product in the air for 1 to 2 minutes, and the temperature difference of ±10 degrees