Hire Veteran Health Heroes Act of 2020 This bill requires the Department of Veterans Affairs (VA) to conduct, as part of the Transition Assistance Program, recruitment for specified medical personnel positions from among medical department personnel of the Department of Defense who hold medical military occupational specialties and are separating from the Armed Forces. Tentative offers may be issued for specified medical personnel positions to applicants who agree to accept the position and meet a preliminary qualification review established by the VA. After the tentative offer process, the supervisor or technician conducting the hiring process must transmit the applicant's information and credentials to the medical facility at which the individual would be hired for final verification and interviews.