PURPOSE: To make a furnace available for quick cooling of products without leak of atmospheric gas, by composing its core tube with a porous sintered alumina tube as an inner tube and a gastight, molten alumina tube as an outer tube.

CONSTITUTION: A core tube 2 is inserted in a heating device 1 of a tubular furnace with a built-in heating element. The core tube 2 is of double construction: a molten alumina tube 3 as its outer tube and a sintered alumina tube 4 as its inner tube, and the clearance between both tubes 3, 4 is filled with refractory material 5. Even when a heated product is transferred from a heating area near the heating element of the furnace to a cooling area outside the heating device, it causes no cracking due to the heat resistance of the sintered alumina tube 4. In addition, the molten alumina tube 3 can eliminate leak of atmospheric gas. As a result, the product can safely be cooled off quickly.