My mate's car has a weak synchro on 2nd, but only when it is dead cold. Unless you put a lot of revs on it in 1st, it just won't go into 2nd. After about half a mile it is OK and will be fine for the rest of the journey. He assures me it has the right oil in it and the right amount.

I'm just curious because I don't know what's going on. It can't be warming up that quickly. What's the likely mechanism for this fault being present on every journey but going away so quickly?

I would have said oil.

You dont say what sort of box, and wether its the matching engine, clutch and Flywheel.

A good number of years ago.... My Mates Sierra 2.9 Box (probably a MT75) did something simmilar. Even with the correct oil in it.
The solution was to change the oil to something else. I think it was either semi or fully synthetic.
It fixed the problem.

I can ask him when I see him.

Plus 1 for oil

Type of oil? I wouldn't have thought of that. One of my thoughts was that it might take the oil a while to be splashed into the right place.

The car is unmodified so it has matching box / clutch etc. It's a RWD manual too.

I changed the oil in my vag 1.9tdi/6speed combo and it did exactly this, have never changed it back as it's got better as the oil got older.

I will add that it was replaced with the vw oem recommended stuff so that wasn't the issue.

It could be the needle roller on one of the gears has partially seized due to lack of oil, in any event the first thing to do is drain & refill with a low viscosity transmission fluid such as MTF94.

The spec of gearbox oil needed is GL4 75W90 and he's been using Castrol Syntrax. MTF94 is GL4 75W80. Is this OK? What difference will the MTF94 make? Does being thinner mean it is less lubricating or that it will splash to where it is needed more easily?

Dragging/sticking clutch will also make gears hard to move

Our 120k mile Alhambra (1.9 tdi / 6 spd manual) was pig to get into 2nd when cold, but good as gold once warmed up. I changed the (probably original) oil for the same grade, but fully synth. 2nd is still not great, but takes less warming up before it's smooth.