A "sun room" with a glass roof is a conservatory - you cannot install permanent heating systems in them AFAICR and, as Trilogy 1982 has pointed out, they fail to moderate extremes of temperature.
Also, proving you can definitely have too much of a good thing- the sheer quantum of light from them causes internal glare problems in rooms adjoining.
The problem with a non-timber frame system and glazing systems are that the rainwater throw uff usually is sealed with - well- sealer.
Its not a welded or formed joint and that leads to leaks over time, especially in our damp Irish climate near tress and bushes.
Push the boat out a bit and do something that will ad value to the house in timber - you'll still need the rising walls.
If yo0u're goign to spend your hard earned cash, invest in design - you know it makes sense.
ONQ.
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Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.