If background noise was the factor, which it's not, but if it was, the background noise to combat would be the thermal noise floor of any physical conductor at any temperature above absolute zero. But that's not the factor. You're assuming the cardiac field is like a radio signal being transmitted rather than a local field effect. A magnetic dipole doesn't radiate energy outward the way a radio antenna does. It creates a static field that exists in the space around it, and that field geometrically collapses with distance. I ran the numbers on Wolfram Alpha, and at 1 meter from your chest the field is around 100 femtotesla. At 10 meters it's around 100 attotesla. At 5 kilometers it's around 10^-27 tesla.

Oh, but you say that you simply cool the sensor to 0K. Cooling helps, but you're still many orders of magnitude short even at near 0K, and you're doing this in Iranian mountains, not a dilution refrigerator.