It could be the computer. It would seem that it’s not getting enough enrichment to sustain running during the warm-up phase.

I understand you can fit a new lock barrel without any other problems.

It’s not likely to be an ongoing problem once you repair or replace the radiator, assuming that is the problem. I would check for other issues, like a blown radiator hose or clamp. There are no other major issues with the Courier that you need to be concerned with, but you do need to understand that it is an old vehicle and old vehicles can break down.