Three ways heat travels
Heat always moves from hot to cold, but it has three distinct vehicles. Conduction passes energy molecule to molecule through a material without the material itself moving. Convection carries energy bodily along with a moving fluid. Radiation ships energy as electromagnetic waves, needing no material at all — which is how the Sun's warmth crosses the vacuum of space to reach you.
Conduction — passing energy hand to hand
Heat a metal spoon at one end and the handle soon warms: fast-jiggling molecules jostle their neighbours, and in metals a sea of free electrons ferries energy along quickly. This is conduction. Its rate depends on the material's thermal conductivity k, the temperature difference across the object, its cross-section, and its thickness. Metals have large k; wood, air, wool and water have small k (they are insulators).
Fourier's law of conduction: the heat flow rate rises with conductivity k, area A and temperature difference ΔT, and falls with thickness L.
Convection — heat rides the fluid
In a liquid or gas, heat can travel by the fluid itself moving. Warm fluid expands, becomes less dense, and rises; cooler fluid sinks to replace it, setting up a circulating convection current. This is how a pot of water heats throughout, how a room's radiator (really a convector) warms the air, how thunderclouds tower, and how ocean currents and the very mantle of the Earth churn. Convection needs a fluid to carry the heat — it cannot happen in a solid or in a vacuum.
Radiation — heat across empty space
Every object, just by being warm, glows with thermal radiation — electromagnetic waves that carry energy away and need no medium at all. That is why you feel a campfire on your face across the air, and why sunlight warms us after eight minutes crossing empty space. The hotter an object, the far more it radiates, and the shorter the wavelength: a poker glows dull red, then orange, then white as it heats. The dependence on temperature is astonishingly steep.
The Stefan-Boltzmann law: radiated power grows as the fourth power of absolute temperature T (in kelvin!). σ is the Stefan-Boltzmann constant; e is the emissivity (0–1); A the surface area.
Because of the fourth power, doubling the absolute temperature multiplies the radiated power by sixteen. An object also absorbs radiation from its surroundings, so the net rate is P = e\sigma A(T^4 - T_s^4), where T_s is the surroundings' temperature. Good absorbers are good emitters (a matt-black surface), while shiny silver surfaces both reflect and radiate poorly — which is exactly why a vacuum flask is silvered inside and why emergency blankets are metallic.
Putting it together, and where this leads next
Look at a single cup of hot coffee and you can see the whole track at once. Its temperature tells you which way energy will flow. It loses energy by conduction through the mug into your hand, by convection as warm air rises off the surface, and by radiation into the room; steam rising from the top carries away latent heat as water evaporates. Its high specific heat is why it stays warm a while. Every effect we met is just energy being accounted for, moving from hot to cold until the coffee reaches equilibrium with the room.
You now have the intuitive half of thermal physics: temperature, equilibrium, expansion, specific heat, latent heat, and the three modes of transfer. The next step turns this into a full theory of energy. The first law of thermodynamics adds work done by expanding gases to heat, making a grand energy-conservation statement; the second law and entropy explain the one-way flow and set the ultimate limit on every engine. And to see why temperature is average molecular energy in the first place, the kinetic theory of gases builds pressure and temperature straight out of colliding molecules. That is where this track leads.