haze on windows - heater core?

[Montyii]

I'm getting a haze on all of the windows in my 85 eta.
I've wiped them down and i see a greasy film/haze after a little while.

I know this points to the heater core, but I'm not smelling anything.
Also ALL of the windows are getting the film.

the care is old and would have thought it had already outgassed. I haven't used any cleaners etc. that could cause it.

I'm just wondering if the fact that all of the windows are getting the haze points to something other than the heater core - thoughts?

If i go the route to change the core and pipes...

I found this on ebay - http://www.ebay.com/itm/Heater-Core-...#ht_1735wt_957

the low cost has me sceptical, but i can replace this 4 times for the cost of the BMW version.

Has anyone tried one of these ebay specials?

[MC Hammered]

Just bumping this to see what you have done for a solution as I am finding an oil film on the windows.

To answer your question about the eBay part, I personally would only want to replace the heater core once and be done with it. So I would buy an OEM part for this job.