Hi Bruce
I am mostly fishing small rivers, but I do on occasion fish larger rivers and I find that the air temperature indicator is just as reliable.
To be fair I am not sure it is the air temperature that affects the Barbel, as you say, why would air temperature make any difference to fish in even one foot of water let alone 20ft of water, it make no reasonable sense at all, that said, I find air temp IS a quite reliable indicator, it is not the only indicator but my average performance has improved markedly since I have been taking note of air temperature.
While air temperature is the indicator I do not believe it is the cause of fish getting on the feed, however if we look to physics we might find the answer.
Guillaume Amontons offered the following theory:-
"The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas' absolute temperature."
This is now known as Amontons Law.
Barbel like all cyprinids have a swim bladder which is controlled in part by a pneumatic valve, they also have a lateral line, an organ for which we do not fully understand, but seems to have a number of sensor cells, some of which can detect pressure.
I am sure Barbel cannot sense air temperature, but I am very sure they can detect minute changes in pressure and it may well be pressure that triggers feeding.
As I said previously I have little scientific proof of this, I have only the result of my experience, but if it is pressure that makes the difference then it will not matter if the rivers are large or small, the laws of physics are the same everywhere.
Obviously except in America where at least one of Newton’s laws of motion is different:-
“For every action there is an exaggerated over reaction!!"
Tight lines.