you have to put in your private key for your ethereum account to mine...?
You have to put your private key into a local .ini file on your mining rig which is read by the mining software and used by the Infura API. Obviously it would be wise to use an eth wallet dedicated for this purpose and which only contains a small amount of eth to cover gas costs. However the key will be as secure as your local system is and it is wise to lock-down mining rigs as much as possible anyway.
This wont be an issue in the very near future once difficulty rises to the point that mining pools are developed. But if you are willing to do so carefully you can take advantage of solo mining at very low difficulty.