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There's nothing uncomfortable or angular about many of the good mid-century designs, things like the eames lounger, the womb chair, the papa bear chair, etc. Perhaps you're confusing more contemporary (80s?) modern design with mid-century. Some of this stuff is expensive though - even the knockoffs.

The wood goods though are not cold at all, and are very warm. Teak is arguably the quintessential mid-century material, and naturally has a nice warm orangey finish. The best mid-century teak goods also feature nice curves and are not at all angular. The price on vintage wood goods is pretty good too. Everything I own was purchased for less than it would cost to purchase similar new, much lower quality, new goods. Ex: My vintage Grete Jalk dining set: $600. The best equivalent (much lower quality) Ikea dining set (Stockholm): ~$1200.

My advice is to avoid the fancy/expensive designers, consider new items for fabric goods (sofas), favor vintage for wood/case goods.