XK-120 winter "topics"

(I almost put "120 winter topics" as the subject, but then thought no one would read it, thinking it was too long.....)

1. Cooling. Going to show on the 5th, I had to pull over while climbing a steep hill to let the car cool off. Was losing power, "popping", and generally performing poorly. Luckily, I was only a mile from the crest, so after 15-20 minutes of cooling off, I made it over the top (by that time, temp was down below 90*C). But clearly, the car needs some attention to the cooling system. Radiator re-cored? New pump that can move the water faster? A guy at the show said something about water running to the back of the block and not getting back up to the radiator while climbing hills - on a 120 he owned in the past, he had modified the plumbing somehow to alleviate this issue. Anyone heard of this before?

2. Warm-up running. There was a GORGEOUS 120 FHC (also SE, I think - wire wheels, dual exhaust) at the show. As he was prepping to leave, he started it up, and it ran at what sounded like a perfect high idle. Owner went about his business while the car warmed. When it was warmed, it dropped off the starting carb and settled into what sounded like a perfect warm idle. My Dad has told me that in all 20+ years he had this car, he could never get it to run that well when cold. The engine idles fine when all warmed up, but even when it should still be warm enough (i.e., it's been shut off for a short while after being fully warmed), I often have to switch on the starting carb (Dad installed a manual switch to control it) to get it to restart. Secrets? Tips? Tricks? My Dad's no dummy, so if he can't get it figured out, doubtful that I will (without some serious help, anyway).

#1 here and my tires are tops on the list for this winter. If I can ever get #2 figured out, that would just be icing on the cake.

Thanks!