How fast do you need to get paint on media blasted parts (heater box)?

[bull]

Can you simply hit these blasted heater box parts parts with some self-etching primer, say 5-6 days after they get blasted, assuming they weren't sitting outside in the rain? What if there's a very slight surface rust starting on them?

While I'm asking, what about the heater core? Would it be a good idea to paint it too?

[Winged 1]

 
Sooner the better painting the parts. Best to be done right after blasting. Be sure to not touch the metal with bare hands. As for painting the core, its copper. No need to paint plus if you do it will loose some of the heat dissipation values.
Eric