Posted by not done it yet on 25/06/2017 12:17:20:
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A couple of pounds extra, for a decent transformer, would likely have been saved on energy use over the period of ownership and it a) would last a lot longer and b) the cost/performance ratio would be favourable for the purchaser rather than the vendor. Routers from ISPs are likely in a similar state – the transformer likely loses nearly as much energy as the router uses.
Transformers are still not designed to run hot, per se. They are designed to cope with the heat generated. Yes, cold running is an ideal situation, but some of these chinese wall warts are only bought by people that either don't know or don't care.
I don't think you can assume that a cool transformer is more efficient than a hot one.
For the same power input, a heavy transformer takes more heat to reach a given temperature than a lighter equivalent. The heavy transformer runs cooler because it has more mass and a greater surface area, not because it's electrically more efficient. The light one runs hotter because it has less mass and surface area, not because it's less efficient.. And the light one will not become significantly more efficient if it's fitted with a cooling fan. It is true that physically big transformers are more efficient than tiny ones, but that's not due to their operating temperatures.
A hot transformer isn't a problem provided the insulation's up to it. Over the years insulation has improved considerably. In the 1920's power transformer temperatures were limited to 65C; by WW2 the limit had been raised to 85C; today, the lowest rating you can get is 100C or 110C (depends on where you are).
So, measuring temperature alone doesn't tell you much. A hot transformer may be operating as per design, or it may be accidentally overloaded, or it might faulty, or, as NDIY points out, perhaps it was under specified for profit. To work out which is the case requires more testing than pointing a thermometer at it.
In a world where consumer electronics are replaced regularly it makes sense not to over specify. Think of all those beautiful high-end transformers ending up as landfill.
Dave