Deterministic database systems have been shown to yield high throughput on a cluster of commodity machines while ensuring the strong consistency between replicas, provided that the data can be well-partitioned on these machines. However, data partitioning can be suboptimal for many reasons in real-world applications. In this paper, we present T-Part, a transaction execution engine that partitions transactions in a deterministic database system to deal with the unforeseeable workloads or workloads whose data are hard to partition. By modeling the dependency between transactions as a T-graph and continuously partitioning that graph, T-Part allows each transaction to know which later transactions on other machines will read its writes so that it can push forward the writes to those later transactions immediately after committing. This forward-pushing reduces the chance that the later transactions stall due to the unavailability of remote data. We implement a prototype for T-Part. Extensive experiments are conducted and the results demonstrate the effectiveness of T-Part.