Flex is designed to be cooled by the air around it with a maximum temperature of 60° and in general to cover flex up including running under carpets is to be avoided.
However my TV draws 115W when in use and 1W on standby i.e. 500ma when in use or 4.3ma on standby with currents so low it is not going to be any real problem if they are not cooled as well as normal. As to changing the cable to something thicker well you could fit a spur and a local socket. All questions like these will have exceptions to the normal which we have not been foreseen. If uncertain I would suggest you get someone local to look at it.
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