Is your Temporary Visitor status that DMV has on file not expired and do you want to renew your license online, through the mail or in an office?
No, I don't want to renew my license. I'm just asking out of curiosity.
What else apart from the DHS documents do I need as a temporary visitor?
You need your New York State driver license, and a permit or non-driver ID card that has 'TEMPORARY VISITOR' on it, among a few other things.