Context : Thermal emission from dust provides a valuable tool for determining important physical properties of the dense structures within molecular clouds .

Aims : We attempt to map the distributions of dust temperature and H _ { 2 } column density of IRAS 05399-0121/SMM 1 , which is a dense double-core system in Orion B9 .
We also search for substructures within the cores through high-resolution submillimetre imaging .

Methods : The source was mapped with APEX/SABOCA at 350 \mu m. We combined these data with our previous LABOCA 870- \mu m data .
The spatial resolution of the new SABOCA image , \sim 3 400 AU , is about 2.6 times better than provided by LABOCA , and is therefore well-suited to our purposes .
We also make use of the Spitzer infrared observations to characterise the star-formation activity in the source .

Results : The filamentary source remains a double-core system on the 3 400 AU scale probed here , and the projected separation between IRAS 05399 and SMM 1 is 0.14 pc .
The temperature map reveals warm spots towards IRAS 05399 and the southeastern tip of the source .
Both IRAS 05399 and SMM 1 stand out as peaks in the column density map .
A simple analysis suggests that the density profile has the form \sim r ^ { - ( 2.3 _ { -0.9 } ^ { +2.2 } ) } , as determined at the position of SMM 1 .
The broadband spectral energy distribution of IRAS 05399 suggests that it is near the Stage 0/I borderline .
A visual inspection of the Spitzer /IRAC images provides hints of a quadrupolar-like jet morphology around IRAS 05399 , supporting the possibility that it is a binary system .

Conclusions : The source splitting into two subcores along the long axis can be explained by cylindrical Jeans-type fragmentation , but the steepness of the density profile is shallower than what is expected for an isothermal cylinder .
The difference between the evolutionary stages of IRAS 05399 ( protostellar ) and SMM 1 ( starless ) suggests that the former has experienced a phase of rapid mass accretion , supported by the very long outflow it drives .
The protostellar jet from IRAS 05399 might have influenced the nearby core SMM 1 .
In particular , the temperature map features are likely to be imprints of protostellar or shock heating , while external heating could be provided by the nearby high-mass star-forming region NGC 2024 .