The　optimization　of　heat　conduction　is　a　critical　task　with　widespread　applications,　and　the　approaches　are　typically　categorized　into　two　main　categories:　thermal　conductivity　distribution　optimization　(TCDO)　and　heat　source　layout　optimization　(HSLO).　While　extensive　research　efforts　have　been　devoted　to　each　of　these　two　categories,　standalone　TCDO　and　HSLO　limit　the　design　possibilities　and　may　lead　to　suboptimal　solutions.　In　this　work,　a　collaborative　methodology　combining　TCDO　and　HSLO　is　proposed　by　transforming　the　collaborative　optimization　problem　into　a　two-level　nested　problem.　In　this　approach,　TCDO　forms　the　inner　subproblem,　tackled　using　the　gradient-based　method,　while　HSLO　constitutes　the　outer　subproblem　addressed　through　Bayesian　optimization　(BO).　The　proposed　method　is　employed　to　solve　two　problem　cases　involving　volume-to-point　and　volume-to-edge　boundaries,　respectively.　The　results　demonstrate　that　the　present　method　is　capable　of　achieving　collaborative　optimization　of　TCDO　and　HSLO　for　both　scenarios　of　continuous　and　discrete　thermal　conductivity　distributions.　Comparing　with　standalone　TCDO　and　HSLO　that　reduce　the　average　temperature　by　[Formula　presented]　and　[Formula　presented],　respectively,　the　proposed　method　achieves　a　significantly　greater　reduction　of　[Formula　presented],　underscoring　its　efficacy.　We　anticipate　that　the　proposed　method　will　serve　as　a　valuable　tool　for　optimizing　heat　conduction　across　diverse　applications,　and　its　adaptable　framework　holds　promise　for　addressing　broader　optimization　challenges.　©　2024　Elsevier　Ltd