For what it's worth, I'm in the UK and have had the problem with the shifter sticking. I had to dismantle the 3 speed one and run a fine file through one of the parts to free it up again. No 200 deg C temperatures in Chesterfield I can assure you!
That's exactly the point. There
have been problems with the shifters but one can be pretty sure that they are
not related to temperature - in opposite to what the very vocal but also very incompetent youtuber claims and other people repeat like a giant echo chamber. The new shifters were invented at the beginning of 2017. Since then until today about 300.000 Bromptons have been made using them. So I am pretty sure only a fraction of them suffers from the problem, otherwise we would have heard about more cases and Brompton would have changed the shifters if a massive amount was affected, simply to safe money if not out of attitude.
If you are hit by the problem the first and easiest approach for a solution is simply to flood the shifter with silicone oil. In many cases this already solves the problem. In case that does not help more massive ways are appropriate like sanding the internals or simply exchanging the shifters on warranty if applicable. It would be interesting to know the age of the bikes affected to find out if it happens trough out production or if the cases are limited to a certain timeframe of production dates.