Check the Firebricks
Firebricks line the inside of the firebox and do two jobs: they protect the steel or cast body from direct flame, and they reflect heat back into the fire to keep combustion temperatures high. They're meant to be sacrificial. Hairline cracks are completely normal and nothing to worry about, so don't rush to replace a brick just because it's spidered with fine lines.
What you're looking for is a brick that has crumbled, has a piece missing, or has cracked right through and shifted out of position. Once the body of the stove is exposed to direct flame, you'll get accelerated corrosion and eventually burn-through of the metal itself, which is a far more expensive repair. Gaps between bricks or bricks that have slumped need attention too.
Firebricks come as either vermiculite (lighter, tan coloured, easily cut with a saw) or dense clay bricks. Vermiculite is cheaper and insulates better but wears faster. Either way, they're inexpensive and quick to swap. Take the old ones out, note the sizes, and if your stove uses a non-standard shape you can often cut a vermiculite board to fit.
