1. A method, in a data processing system having a plurality of processors and a memory, for handling conflicts in a transactional memory system, comprising: executing, by the plurality of processors, threads in the data processing system in a first conflict resolution mode of operation in which the threads execute conflicting transactional blocks speculatively; determining, by a processor of the plurality of processors, for a transactional block, whether the first conflict resolution mode of operation is to be transitioned to a second conflict resolution mode of operation in which the threads accessing the conflicting transactional blocks are executed serially and non-speculatively; executing, by the processor, a thread that accesses the transactional block using the second conflict resolution mode of operation in response to the determination indicating that the first conflict resolution mode of operation is to be transitioned to the second conflict resolution mode of operation; and determining whether or not to transition the transactional block back from the second conflict resolution mode of operation to the first conflict resolution mode of operation, wherein the determining whether or not to transition the transactional block back from the second conflict resolution mode of operation to the first conflict resolution made of operation comprises: maintaining, in the transactional block profile entry, a transition counter identifying a number of accesses to transactional blocks having a same classification associated with the transactional block that have occurred since the transactional block was transitioned to the second conflict resolution mode of operation; determining whether the transition counter has a value that meets or exceeds a predetermined threshold; and transitioning the transactional block from the second conflict resolution mode of operation to the first conflict resolution mode of operation in response to the transition counter having the value that meets or exceeds the predetermined threshold.