I don’t think that this was a figment of your CP’s imagination as I had the same limitation at a previous airline. The wording was from memory that assumed temp is prohibited with a “Marked temperature inversion” ie a large inversion. I always thought that the reason was because of the windshear as you fly through the inversion layer, so this is just an extension of the “prohibited with windshear” limitation.
Like many other things in company manuals, this limitation is probably something which was present in an earlier version of the FCOMs, (like TR voltage range or max generator rise, etc). It was probably removed by Boeing either because it was found to be no longer necessary or was downgraded to a caution or info rather than a limitation and your airline has left it in.
If a limitation is there in print in your company manuals it is a bold (or bored!) manager that takes it out without checking the references, it might have been left in because it was too difficult or time consuming to investigate or maybe just had not been noticed because everybody there assumed it was still valid. I apologise if I am doing your airline a disservice but this is often how things work in practice. I bet this is still in many other 737 ops manuals around the world.
S&L