A building or component thereof comprising at least one building exterior wall with a first side which is an outside and an opposing second side which is an inside, wherein, on the second side of the building exterior wall, there is at least a first thermal insulation with a side facing towards said second side of the building exterior wall and a side facing away from said second side; at least one linking part extending from the second side of the building exterior wall in the form of a linking wall, a linking floor and/or a linking ceiling, wherein the first thermal insulation on the second side of the building exterior wall extends substantially up to the linking part, such that the first thermal insulation and the linking part form a corner region; at least one heat conductor, wherein this heat conductor has a higher thermal conductivity than the first thermal insulation, wherein the heat conductor comprises or constitutes a corner profile with a first limb as the first portion or as a component thereof and a second limb as the second portion or as a component thereof, wherein, at least in portions, the heat conductor is mounted or positioned in the corner region such that thermal energy is transferable via this heat conductor into said corner region, wherein the first portion of the heat conductor is thermally conductively connected to the second portion of the heat conductor, and wherein the first portion extends at least in places along the first thermal insulation and wherein the second portion extends at least in places along the linking part, wherein the first portion of the heat conductor is indirectly or directly connected to the first thermal insulation, wherein the second portion of the heat conductor is indirectly or directly connected to the linking part, wherein the heat conductor has an extent beginning at or adjacent to the linking part along the first thermal insulation adjacent to or on the first thermal insulation and wherein the heat conductor has an extent beginning at or adjacent to the first thermal insulation along the linking wall adjacent to or on the linking wall. at least one building exterior wall with a first side which is an outside and an opposing second side which is an inside, wherein, on the second side of the building exterior wall, there is at least a first thermal insulation with a side facing towards said second side of the building exterior wall and a side facing away from said second side; at least one linking part extending from the second side of the building exterior wall in the form of a linking wall, a linking floor and/or a linking ceiling, wherein the first thermal insulation on the second side of the building exterior wall extends substantially up to the linking part, such that the first thermal insulation and the linking part form a corner region; at least one heat conductor, wherein this heat conductor has a higher thermal conductivity than the first thermal insulation, wherein the heat conductor comprises or constitutes a corner profile with a first limb as the first portion or as a component thereof and a second limb as the second portion or as a component thereof, wherein, at least in portions, the heat conductor is mounted or positioned in the corner region such that thermal energy is transferable via this heat conductor into said corner region, wherein the first portion of the heat conductor is thermally conductively connected to the second portion of the heat conductor, and wherein the first portion extends at least in places along the first thermal insulation and wherein the second portion extends at least in places along the linking part, wherein the first portion of the heat conductor is indirectly or directly connected to the first thermal insulation, wherein the second portion of the heat conductor is indirectly or directly connected to the linking part, wherein the heat conductor has an extent beginning at or adjacent to the linking part along the first thermal insulation adjacent to or on the first thermal insulation and wherein the heat conductor has an extent beginning at or adjacent to the first thermal insulation along the linking wall adjacent to or on the linking wall.