The hot side does not need a "masternode start," as this happens automatically as long as the dashd is running (see Lucas_Jackson's post above to make sure it is always running).

However, if it was offline too long (say, if the VPS service was down for a couple hours), the auto-start script will not be able to prevent your MN from being kicked off the list and you will need to issua a start from the cold wallet.

Currently in Dash Core there is no way to issue a masternode start without exposing your cold-side 1000Dash private keys to a computer connected to the internet.  Evan has said before that he is working on a way to keep the 1000Dash on a computer that never touches the internet, but I have not heard anything more about it.  We may have to wait until Electrum-Dash adds support for MN so we can use either a hardware wallet or Electum's watch-only+offline transaction signing functionality to offline start MN).