Should Auto Disco get so hot

I have a 1996 discovery es 300tdi, currently living in spain 12 miles from coast but 910 metres above sea level, the transmission hot light comes on approximately half way up the hill (500 metres in altitude)when towing a 1 tonne trailer. The temperature is usually about 30 degrees C. Is this normal, I have changed transmission oil but not much change. Do I need a larger oil cooler or is it likely a transmission overhaul? The red light doesn't go out until i get home and let it rest, the last mile having 200 metre height gain and no tarmac.
Any help much appreciated.

Have you tried dropping into third or second manually to stop auto box changing up to soon.?Try locking in a low gear.

wouldnt that put more strain on the engine then and making that get hotter??

Thanks for your replies.
Have tried dropping gears, no change, i suppose thye gearbox works faster if not harder. Have tried going slower, going faster not really an option, it's quite a hill. Someone suggested adding an electric fan to increase airflow over cooler. The gearbox functions perfectly, I assume if there were problems in the box they would make themselves known by poor shifting nasty noises etc. I am new to auto boxes so just guessing.

RAZ8550TDI said:

wouldnt that put more strain on the engine then and making that get hotter??

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It's the gearbox shifting up and down that heats it up (although not necessarily in this case). Standard advice on an auto box is to shift down when towing a load uphill (or, of course, downhill, but for different reasons!). Shifting down stops the box "hunting" between gears.

On my auto I lock it in 3rd between 30 and 50 and 2nd when slower than 35 for most of the time. You then get a more direct feel and there is no slip in the box so less heat is generated. Engine may spin more but thats fine as light throttle pressure and moderate revs means low fuel use! Try it for a week and see. It took me a long while to get used to my auto especially when towing. Most of the time this is 3.5 ton which work the box hard unless i lock it in a lower gear.

PASTMASTER said:

It's the gearbox shifting up and down that heats it up (although not necessarily in this case). Standard advice on an auto box is to shift down when towing a load uphill (or, of course, downhill, but for different reasons!). Shifting down stops the box "hunting" between gears.

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that wasnt an answer to what you qoated

When you think about it that almost made sense

RAZ8550TDI said:

that wasnt an answer to what you qoated

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Sorry. I withdraw my answer. I thought the original query was about the box getting hot, not the engine. The engine cooling sustem should be able to cope with the extra strain.

Thanks for advice.
Drove the hill empty today using the gears not changing up until revs nearly 3000 to limit torque converter, no red light, the air temp was only 28 today (though it was 33 at the bottom of the hill)... in August it should warm up a bit. The engine never gets hot, only warm when the AC is on when going up hill (not used if i am on my own). might look at fitting a fan in front of the oil cooler or getting a bigger oil cooler to limit damage to the box, good idea or waste of money?

PASTMASTER said:

Sorry. I withdraw my answer. I thought the original query was about the box getting hot, not the engine. The engine cooling sustem should be able to cope with the extra strain.

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what i should have explained better is that if he used higher gears low revs he will only use more throttle, more air more fuel bigger bang more heat