Volcanoes are the planet's most obscene heat leaks. Kīlauea alone bleeds around 10¹⁰–10¹¹ W of thermal power into the atmosphere continuously — comparable to a hundred nuclear reactors, dumped straight to sky. Geothermal wells only nibble at that budget. What if, instead of drilling around a volcano, we straddled a fumarole with a kilometer-tall stack and turned it into the world's largest solar-updraft-tower-but-hotter?

The physics is embarrassingly favorable. A tall chimney over a hot vent generates a "stack pressure" from buoyancy:

ΔP ≈ ρ_amb · g · H · (T_hot − T_amb) / T_hot

With H = 1000 m, T_hot ≈ 1100 K (fumarole gas ~800 °C), T_amb ≈ 300 K, ρ_amb ≈ 1.2 kg/m³:

ΔP ≈ 1.2 × 9.81 × 1000 × (800/1100) ≈ 8.6 kPa

That's roughly a 90-cm water column of free draft — no fan required, forever. Push it through a 100-m-diameter throat (A ≈ 7,850 m²) with hot-gas density ~0.3 kg/m³, and even after slowing the flow to extract useful work, mass throughput lands near ~500,000 kg/s. The thermal power carried up the shaft, Q = ṁ·c_p·ΔT ≈ 5 × 10⁵ × 1000 × 800 ≈ 400 GW. Real turbine efficiency (Brayton-ish, hot inlet, cool ambient sink) sits around 25–35 %, so a well-behaved stack could theoretically export 100–140 GW — the electrical draw of France.

Then reality shows up wearing a hazmat suit.

• The gas is a nightmare. Volcanic plumes carry SO₂, H₂S, HCl, HF, and fine ash. HF eats glass; HCl eats steel; ash sandblasts turbine blades at 200 m/s. Even Inconel 625 corrodes within months in a Kīlauea-type plume. You'd need SiC-coated ceramic-matrix-composite blades, and scrubbers upstream that themselves cost gigawatts of pumping.
• The stack must survive its own draft. 8.6 kPa across a 100-m throat is 68 meganewtons of net upward suction on the roof of whatever caps the vent. The chimney wall itself sees hoop stresses from thermal expansion of a 1-km column heated to 800 °C on the inside and 20 °C on the outside — a Δ that will crack any monolithic material. Answer: a double-wall design with a refractory Al₂O₃–SiC inner sleeve and a prestressed concrete outer shell, cooled by a rising annulus of clean air (which you can also run through a bottoming Rankine cycle — free 5 GW).
• The volcano won't cooperate. Vents migrate. Eruptive phases can raise gas temperature 400 °C in hours or slam the tower with pyroclastic flow at 700 km/h. A single Vulcanian burst delivers ~10¹⁵ J — enough to vaporize the throat. You'd need a blast-relief valve the size of a football stadium and seismic isolators rated for Mw 6.
• Foundations on lava. Fresh basalt has bearing capacity ~5 MPa but is riddled with lava tubes. Your 400-meter-diameter ring foundation (~2 million tonnes) has to be piled onto older, cold basement rock 100 m below — a real problem at Icelandic and Hawaiian sites, easier at Ol Doinyo Lengai.

Best candidate: Erta Ale in Ethiopia — persistent lava lake, boring plume chemistry (relatively low HF), remote enough for a 100-GW HVDC line to Djibouti's grid. Realistic derating for corrosion downtime, turbine bypass during eruptions, and gas cleanup: maybe 10–15 GW average delivered. Still four Hoover Dams from one hole in the ground.