You've actually asked quite a lot of questions here, and the answers can be modeled fairly simply using "heat transfer" fundamentals. Additionally, it's good to

You've actually asked quite a lot of questions here, and the answers can be modeled fairly simply using "heat transfer" fundamentals. Additionally, it's good to know that heat can lost in space by converting to photons and emitting those photons from the object as "blackbody" (colloquially "infrared") radiation. Light/radiation/photons can travel through a vacuum so that's how heat leaves an object in space, and how some heat leaves earth. Your thermos example is a bit confusing because it's a thin wall. For understanding heat transfer it's better to use medium thickness walls. It's hard for me to come up with a real-world example that we'd have intimate familiarity with because we can't typically reach inside a solid material with our fingers. I'd like to point out this illustration[0] though, which is used in many university textbooks for introduction to transport phenomena (the study of mass and heat flows). If you have a near-perfect insulator and expose one side to heat, the other side will remain cool. Between the one side and the other, the temperature must gradually change from hot to cold. The earth is a pretty big insulator, so it keeps most of the core's heat in, and makes the surface much cooler than the core. Different layers of the earth have different properties, so the "steepness" of that transition from hot to cold changes suddenly at certain depths where the earths material changes. You can see Earth's temperature gradient here[1]. Definitely, if Earth absolutely could not get rid of its heat, eventually all the layers would be the same temperature. However, enough is lost to space each year to keep the surface "cool". It's actually a very, very, very tiny amount of the heat that is lost to space. The temperature of the core is 5000K-7000K but has only lost 250K over the past 4.5 billion years. Evidently the earth is a particularly good insulator. I used to help drill pretty deep holes in earth, going down 5,000-10,000 feet or more. Temperature of the earth at that depth could be actually quite hot, like 250-350 degF. 0: (Image of a simple thermal profile through a medium thickness wall of uniform material) https://ars.els-cdn.com/content/image/3-s2.0-B9780124158917000121-f12-03-9780124158917.jpg https://ars.els-cdn.com/content/image/3-s2.0-B97801241589170... 1: https://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Temperature_schematic_of_inner_Earth.jpg/275px-Temperature_schematic_of_inner_Earth.jpg https://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Te... 2: (Energy balance of earth) https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget 3: (Solar energy balance of earth) https://www.weather.gov/jetstream/energy https://www.weather.gov/jetstream/energy