Yes, good point.
The SMPS is only slightly warm.
BTW. I see BT call this HomeHub2
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Just a word of caution make 100% sure that any LPSU you get is at least 230 v (240 V would be better) as many of the China made ones while they will claim they are 230 v they are almost always 220 V . Now if you are powering a DAC or Pi or other item this may not matter as you switch the item on and use it then switch it off . However things like Routers tend to be left on 24/7 and those 220 v units will not only run hot but very likely fail after a few weeks continued use. You need to have a really good quality unit that will not have problems being on all the time and sadly that often means costly .
I have looked into replacing this device on my BT Home Hub 2 , beware the DC plug is a non standard size not supplied in the iFi power switches.
FYI
DC Right Angle Connector
Inside Diameter 3.0mm
Outside Diameter 5.50mm
Input 230V 0.3A
Output 12.0V 1.5A
I would be interested if anyone else has replaced one of these.
bump
Final solution was to replace the router with a TP-Link TL-Link Archer VR400 V3 AC1200 and iFi power supply.
This has solved the original issue and enabled (so far) a more stable internet, I was getting quite regular drop outs with the Home Hub 2.
I guess like most ISP's BT provide the cheapest hardware they can get away with.