Warning: Do not watch the video if you don't like looking at exposed human organs.
Instead of transporting hearts in an ice cooler and hoping that they don't become unusable while you're at the tailgate, a company called TransMedics developed an organ care system (OCS) that keeps the organ alive and operating in an artificial environment while being transported.
They also have an OCS for lungs, but it's not as cool to watch as the one for the heart, as the lungs don't appear to move. Again, as a warning, this video has graphic visuals of human organs:
The TransMedics website indicates that they also have OCSs for kidneys and livers, but I didn't see any videos for those.
It's like magic.