Serial numbers of engine/chassis not matching would devalue it for some. Some may not care.

It would take months to make enough condensate to freeze again, if the thermostat is working. If it was mine I would inspect it annually, and go from there based on what I found. If there was no paste in the separator then there would be nothing to freeze.

__________________
2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue