The words hot soft recur is several songs The Hold Steady songs. The words can be said to be a description of flesh and human bodies, but is also the antonym of the more well known phrase "cold hard", as in "cold, hard facts" or "cold, hard cash".
The use of the term in Boys and Girls in America may also be a self reference to when the term was first used in Most People are DJs. In Most People are DJS, the term is a description of people in juxtaposition to the hard rock of the planet we live on.
In Hot Soft Light, the hot soft light is at the centre of a cross, showing that the term also has religious significance. This describes Jesus on the cross - "hot soft" indicates he is flesh but the "light" would imply the divine.
In First Night, the term hot soft eyes seems to imply a physical attraction, which could again be tied to a description of human bodies.