converted into luminous energy
When hitting a surface this luminous energy, which is just radiation, will be absorbed and thereby converted into heat to raise the internal energy of the surface.
If it doesn't hit anything - maybe it is send out into space - it never changes form.
and heat energy
By heat energy you might mean internal energy.
Energy transport is one thing: Heat up the air in your house (that is, raise the thermal energy), and open the windows, and the warmer air escapes. The warmer air will be mixed with ambient air and heat that up. This is just an exchange between air molecules to reach a common state of internal energy - no energy tranformations here, just transport from one air molecule to another.
Energy conversions is another thing: Any particle with internal energy (a temperature above $0 \:\mathrm{K}$) will emit radiation to some degree. So, at some point the heat of the air will be emitted away from the air into outer space (only to be absorbed by something else, should it ever hit anothor particle, an be reconverted into internal energy by heating that particle).
The circle of life: Of course other conversions will happen also as a consequense. The temperature differences of different layers of the air in our atmosphere causes winds (changes in kinetic energy and gravitational potential energy), causing wind turbines to turn (mechanical energy again and then converted into heat and electrical potential energy).
It goes around, and around, and around. Only when energy leaves the planet the cycle is finished (unless some space object absorbs it and emits it back).