Wow. Do they really make that much difference.
Lack of airflow is definitely the primary problem at idle, IMO. You could certainly have other problems as well, but airflow is the weak link with the stock setup at idle. With my previous 270 sweep temperature gauge, I could literally see the needle drop when the electric fan came on, and even it doesn't move all that much air.
But (again IMO) if you have problems with running hot at speeds of 30 mph or more, more fan is not likely to help.
From my discussions with an ex-dealer in the US, it seems that the "tropical fan" was never actually listed as an option for the TR3; just something that dealers in Australia discovered would fit and work. It's still not clear to me that the fans pictured are, in fact, the same fans that were installed back in the 50s. PN 211986 seems to have been introduced some time after 1960, and was the stock fan (or at least listed as an option) on several Triumph models including TR4A, early Vitesse/Sports 6, Triumph 2000 and early GT6.
As a side comment, my father's opinion is that the stock 4 blade fan tended to twist in use and lose pitch from what they were originally. It makes a certain amount of sense to me. And he claims to have solved his idle cooling problem by carefully tweaking more pitch into the 4-blade fan (making sure that all blades are bent the same, to avoid introducing vibration).
Also, there is a 6 blade Volvo fan that can supposedly be modified to work on a TR. Just redrill two holes in the right places. Bob Schaller wrote of what I assume is a different Volvo fan, that "fit perfectly" but required the fan extension to be shortened.