No, outside help of a third party (keeping the key) or normal programming techniques (i.e. wiping the key using a timer) there is no key that has such an intrinsic time out.
Certificates have a validity period though. With such a certificate it is possible to sign messages, adding the certificate to the signed message. You then only accept those messages whose certificate has not expired. In other words, the key itself will still be available, but it has become useless.
For this use either the PGP or CMS container formats, which are able to store the certificates as well as the data and the signature. The data may be encrypted as well.