There should not be much difference.
I think the only thing that would alter heat loss, would be if the new area now gives the whole space more outside/external walls or if the roofing/ceiling materials differ, but if both rooms were calculated correctly originally, you would expect that to more or less even it's self out. But always best to do the calcs and see if you have efficient heat.
If Mary has two oranges, and a bear sh!ts in the woods, will little Jonny be able to make his unicorn fly?
Not a clue? Exactly. Need to know the U-value of the French doors for a start. Removing the doors will almost certainly be in breach of Building Regulations though, so you'll need to put them back if you ever want to sell the house
Good thing is, you can test it.. Leave the doors open during winter and see a) how comfortable the room is that is linked to the conservatory and b) how much the gas bill goes up by. My bet is you won't convert it to an opening
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