The　furnace　temperature　(FT)　control　is　the　key　for　ensuring　the　stable　operation　and　effective　pollution　reduction　in　municipal　solid　waste　incineration　(MSWI)　processes.　However,　conventional　control　strategies　encounter　challenges　in　effectively　managing　FT　due　to　uncertainties　associated　with　material　composition,　feeding　modes,　and　equipment　maintenance.　In　response　to　these　challenges,　this　article　introduces　a　control　approach　utilizing　a　Bayesian　optimization-based　interval　type-2　fuzzy　neural　network　(BO-IT2FNN),　which　achieves　offline　optimization　and　online　control　through　the　FT　controller　constructed　by　IT2FNN.　In　offline　optimization　process,　the　BO　algorithm　is　used　to　optimize　the　learning　rate　of　multiple　types　parameter　of　IT2FNN　controller.　In　the　online　control　process,　fine-tuned　by　gradient　descent　method　with　multiple　LR　for　adaptability.　In　addition,　the　stability　of　control　system　is　confirmed　using　theorem　of　Lyapunov,　providing　the　theoretical　foundation.　Experiments　with　real　MSWI　data,　tested　on　a　hardware-in-loop　platform,　prove　the　effectiveness　of　the　proposed　method.