Fuel related for sure.

Warm Up Regulator(WUR) - it has a bi-metallic strip that heats up and changes the fuel pressure as it warms (in unison with the engine). In these temps at the mo, going from fully cold to warm-ish will prob take 5mins, so it tallies up.
They are easily stripped and cleaned up, but doing that is useless if you've got no way of validating the pressures. You can easily make a DIY fuel pressure tester for these, and you'll be able to see the pressure behaviour as it warms up. It works backwards to how you'd expect if you're measuring between WUR and metering unit - cold it will be around 1.3bar, warm you should expect around 3.6bar. A strip and clean doesn't always do the trick - but again rebuild kits are available - or just get a known good unit.

If the CO adjustment screw in the metering unit is well and truly out of whack, it might be able to run when cold but die due to leaning or going too rich when warmed slightly - I haven't seen this extreme myself but theoretically its possible. A friendly MOT tester with the kit could probably help out here as they can measure what its doing. Easily adjusted via allen key.

Lastly, it could be a sticky metering unit flap - millions of articles written about this (don't worry whether its xr3i specific - just K-Jetronic Metering Unit) so I won't repeat all that. If you try and rev it when its cold (and running), does it stutter, or does it rev cleanly and come back down to idle cleanly? If yes, then I'd doubt its this, but again its all easily checked and cleaned up.