I have the private key, do I use the chronomint application to sweep my private key to move these coins to hot wallet where I can have direct access to these coins?
You have a direct access to your tokens now because you have your private key.
ChronoWallet is a client-side wallet where you own and control your private keys. We never store any private keys. So ChronoWallet can be considered a cold storage too. When exchange or any other service owns your assets private keys it can be called a hot storage.
You can use your current private key to access your tokens with ChronoWallet. However, the more secure way is using your wallet file (it is called 'keystore/JSON file' in MyEtherWallet), mnemonic key or ledger nano.