Hello there:
for such simple thing like a bottle warmer I would not waste time and money to design such complex circuit. Try one of the following:'
1. There are coffee-cup warmers available on the market; they run ~10W, 110 VAC, and the coffee is kept at ~ 60 deg.C.
2. If you remove a bimetal thermostat from a discarded iron, this can be adjusted to temperatures from 40 to 120 deg.C; the contact is rated to 110 VAC and ~1 kW, so you can use a suitable heating resistor and any voltage from 3 VDC to 11V AC.
3. Some dealers offer PTC devices, solid-state temperature-sensitive resistors. you can select one with a suitable temperature and in series with a heater resistor in a 12 to 24 VDC circuit, it will work for years. No contacts, the current stops at the threshold temperature and starts below.
---------- Post added at 22:58 ---------- Previous post was at 22:57 ----------
Under point two above, the voltage range should read 3VDC to 110V AC.