In blockchains such as Bitcoin and Ethereum, transactions represent the primary mechanism that the external world can use to trigger a change of blockchain state. Transactions serve as key sources of evidence and play a vital role in forensic analysis. Timed transaction refers to a specific class of service that enables a user to schedule a transaction to change the blockchain state during a chosen future time-frame. This paper proposes T-Watch, a decentralized and cost-efficient approach for users to schedule timed execution of any type of transaction in Ethereum with privacy guarantees. T-Watch employs a novel combination of threshold secret sharing and decentralized smart contracts. To protect the private elements of a scheduled transaction from getting disclosed before the future time-frame, T-Watch maintains shares of the decryption key of the scheduled transaction using a group of executors recruited in a blockchain network before the specified future time-frame and restores the scheduled transaction at a proxy smart contract to trigger the change of blockchain state at the required time-frame. To reduce the cost of smart contract execution in T-Watch, we carefully design the proposed protocol to run in an optimistic mode by default and then switch to a pessimistic mode once misbehaviors occur. Furthermore, the protocol supports users to form service request pooling to further reduce the gas cost. We rigorously analyze the security of T-Watch and implement the protocol over the Ethereum official test network. The results demonstrate that T-Watch is more scalable compared to the state of the art and could reduce the cost by over 90% through pooling.