In air and water convection is the major heating process. Thick insulation makes temp. AND it traps air to eliminate convection. At low temperature radiation is small, but if all other heat mechanisms have been reduced, then it can be the biggest remaining energy loss mechanism. That is why thermos bottles work so well at retaining thermal energy.
All objects emit radiation.
The amount of energy they emit this way depends very strongly on temperature. It is not emitted as a single wavelength, but as a whole spectrum. We experience different regions of the spectrum in various ways. Entropy of a system must always increase. A single object can lose entropy, but only if the outside world gains more.