I think I blew it up

With my nightmare of a registration process done and over with, I decided to celebrate by taking my new to me 325is out for a drive. Which was cut short by an over-heating issue (imagine that).
Temp gauge told me it was pretty hot (but from reading the stickys, it may have been hotter), but after pulling over and filling the coolant which was so graciously puked all over my engine bay, I let it cool down and it ran and drove fine no over-heating after that.
Took it out for another drive, to which after awhile I experienced another overheating issue (didn't get nearly as hot as last time as I made sure to stay close to home), it would seem that it is spewing coolant out of the overflow in my expansion tank onto my radiator fan. Now I'm just waiting for next paycheck to order everything to completely over-haul the cooling system.

But main question being, with it getting so hot the first time, what are the odds I warped/cracked the head? It seems to run fine with no white smoke bellowing out the tail-pipe, or any crazy bubbling expansion tank. Would it be stupid of me to tear it down anyways or is there any checks I can do in the mean time while I wait to get it into a shop for a leak-down test?

I'm definitely starting to learn the meaning behind "The most expensive car is a cheap BMW"

While severe overheats put you at high risk of head or head gasket damage, it's not a certainty. Two tests you can do to see if there's any damage. Compression test to verify no leakage from the combustion chambers, and cooling system pressure test to ensure there's no cooling system leaks. If both of those come out OK then you've dodged the bullet.

Apologies for any dumb questions, I'm entirely new to working on European cars. 99% of my experience is fixing domestics.
From what I found in that guide in the sticky, I should be looking for about 145-160psi in each cylinder, right?

Correct. 145 would be considered low.

Sounds good! I'll run these tests later in the week when I have a couple days off and report back with what I figure out!

As DC said damage is certainly not a certainty (ask me how I know). If engine is operating normally you could just monitor it for a while - checking for any coolant in the oil, continued loss of coolant, white smoke. You may see the need to add coolant a bit at a time for awhile as all the air works it's way out. This is different from coolant loss as it's just filling in where there was air. The probable appearance difference is that a blown gasket or cracked head would have a more steady loss related to how long and hard you are driving. Just my guess but only thing for immediate concern and action is if you see coolant in the oil. Maybe more danger to watchful waiting that I don't appreciate and DC or Horns can point it out.

Why wouldn't I just run the tests ? Learned a long time ago not to "fix" it if it ain't broke and getting a bit lazy in my wonder years.

Originally Posted by john kaminski

As DC said damage is certainly not a certainty (ask me how I know). If engine is operating normally you could just monitor it for a while - checking for any coolant in the oil, continued loss of coolant, white smoke. You may see the need to add coolant a bit at a time for awhile as all the air works it's way out. This is different from coolant loss as it's just filling in where there was air. The probable appearance difference is that a blown gasket or cracked head would have a more steady loss related to how long and hard you are driving. Just my guess but only thing for immediate concern and action is if you see coolant in the oil. Maybe more danger to watchful waiting that I don't appreciate and DC or Horns can point it out.

Why wouldn't I just run the tests ? Learned a long time ago not to "fix" it if it ain't broke and getting a bit lazy in my wonder years.

The main reason to run the pressure test on the cooling system is coolant is not a very good lubricant for main, rod, and cam bearings, so if you've got an oil system to coolant system breach you really don't want to run the engine that way. Cooling system to combustion chamber breach is a bit less dire, but you do have to be concerned about getting a hydro lock if you get too much coolant into a cylinder when the engine shuts off.