The invention provides a color conversion arrangement, a lighting unit, a solid state light emitter package, a luminaire and a specific use of a graphene layer. A color conversion arrangement (140) with the first aspect comprises a first luminescent layer (110), a supporting layer (106) and a first graphene layer (108). The color conversion arrangement (140) is for converting light of a first color to light of another color. The first luminescent layer (110) comprises a first luminescent material which absorbs a portion of light of a first spectral distribution comprising the first color and converts at least a portion of the absorbed light towards light of a second spectral distribution. The supporting layer (106) supports the luminescent layer (110). The first graphene layer (108) thermally conducts heat in a lateral direction such that temperature differences in the color conversion arrangement (140) are reduced. Different arrangements of the layers of the color conversion arrangement (140) are provided.