Moving a 5,000 vinyl LP collection safely

@milanos.  No way would I ship them flat!  I'm no expert but records stored for decades on edge don't warp.  There was a guy on AK that experimented with horizontal storage with poor results toward the bottom of the stack IIRC.  I don't think there is anything to gain.  I get nervous if I leave records laying horizontally for more than a day or two. 

I had a few records lying flat for years - nothing happened.

Well then that is what I'd do.  Ignore millions of vertically stored records that aren't warped after decades and do as inna suggests.  

No, I don't suggest it, I store records vertically, I simply had in storage a few lying flat.

Thank you all for your advice! Much appreciated. Where we seem to be netting out:

— Yeah, records used to be shipped in vast quantities to record stores - remember record stores? - in all kinds of conditions, many probably far worse than this. But these are MY records.
— All discs are packed vertically, tight but not squished, in 72 single-sided boxes. All seams are taped with strong plastic shipping tape. They are stacked 4 high. Nothing has started to collapse.
— The 83 degree temperature, for a two hour distance, seems non-threatening.
— I will make sure that the boxes are stacked and strapped so that they cannot move.
— I will move the 78s myself
— And last but not least, the mover just said he is a vinyl collector himself, he is assigning his son to this move to keep an eye on it.

It seems that you cannot get moving insurance without first making an inventory of each and every record. That would mean not moving until December! At least I wouldn’t have to worry about the truck getting hot then.

lewm, I’m moving from NoHo, now the 2nd most expensive residential area (folks who are or once were my "neighbors" are Nora Jones, David Bowie, Keith Richards, Denzel Washington, to name a few) in New York City, to The City of Newburgh on the west bank of the Hudson River. Newburgh is known as the Murder Capital of NY State (Preet Bharara’s first big bust was of a couple of major drug gangs there some 12 years ago: he rounded up over 40 people in one big bust together with the FBI). But since Newburgh also sports the second largest Historic District in the State with gorgeous brick townhouses at prices that are far less than what you would pay in Brooklyn, who cares? When I moved to NoHo in 1976, NoHo was not exactly the safest place in the world either, so this is sort of a going home. Lots of fellow artists are moving there: we like edgy, inexpensive places where there is a sense of community and where we can work collaboratively and where we can afford to experiment. And, it is quiet at night, no noisy bridge and tunnel people (what snobby NYer’s call the folks who come into the city in the evenings and weekends from the suburbs), no gawking European and Japanese tourists. The ground doesn’t vibrate. The night air has a fresh snap to it.

I will let you all know how it goes!