Yes, bed bugs can live anywhere that there is a host for them to feed off of - in other words, anywhere.
They feed mostly off of humans and animals. They are called 'bed' bugs because people are often in bed for long uninterrupted amounts of time for them to be able to feed.
If you think you have bed bugs, know the signs, buy mattress and clothing covers before they get into your bedroom... Prevent them before they get to you!
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Bed Bugs can apparently live anywhere. They mostly choose to live very close to their food, that's why they are usually found in beds, bed frames, and couches.
But I will add that if the oven is in use, anything living inside the oven is going to be killed by the high temperature. If you never use your oven, then yes, things could be living there.