Hi,
how about a small PTC thermistor? As the temperature goes down it will draw more current and heat the bottle. If it's a glass bottle, just attach it to the outside and insulate the bottle. For a plastic bottle you would be best attaching it to a small metal plate bent to fit the curve of the bottle.
By correct choice of thermistor and supply voltage you can adjust the temperature. Electrically you just connect it to a supply, AC or DC, a small mains transformer would be ideal.
G8RPI.