The difficult part is finding some place to put your device where it can transmit data that everyone can receive, but it can not be otherwise accessed. ("Recipe for unicorn soup: First, catch a unicorn...") However, there are some possibilities. On the Moon would be good for a decade or so. Even an ordinary orbit, with "destruct if anyone gets close" circuitry, would be a possibility.
Now, the easy part. Generate a bunch of ginormous public/private key pairs, one for each day of secrecy expiration you want to provide with this device. Store the private keys on the device, programmed to continuously transmit all expired private keys. Publish the public keys.
Now, to encrypt something to be revealed on January 1, 2038, you just encrypt it with the "January 1, 2038" public key. Not even you can decrypt it until the private key is transmited by the repository.
Of course, there is the itty bitty trust issue that the entity making the device didn't keep a copy of the private keys.