A glassmelting method comprising passing heated glassmaking material into a glassmelting furnace; combusting fuel with oxidant having an overall average oxygen content of at least 35 vol.% oxygen to produce heat for melting said heated glassmaking material in said glassmelting furnace and produce hot combustion products having a temperature greater than 982.2 °C (1800 °F); withdrawing said hot combustion products from said glassmelting furnace and feeding said hot combustion products into at least one first passageway of a heat exchange unit, wherein the temperature of said hot combustion products entering said at least one first passageway is at least 982.2 °C (1800 °F); flowing said hot combustion products through and out of said at least one first passageway; feeding glassmaking material into and through at least one second passageway of said heat exchange unit separated from said at least one first passageway by a barrier through which said glassmaking material and said hot combustion products cannot pass and through which heat from said hot combustion products passes to said glassmaking material to form said heated glassmaking material, with the at least one second passageway surrounding the at least one first passageway; and maintaining, by selecting the geometry of the first passageway(s), the total heat exchange surface area of the barrier and the distance of at least one inlet nozzle of the hot combustion products in the at least one first passageway from the barrier, the heat flux from hot combustion products in said at least one first passageway to said barrier sufficient that the temperature of the surface of said barrier that is in contact with said glassmaking material does not exceed 871.1 °C (1600 °F) and that the temperature of said glassmaking material does not reach or exceed the temperature at which the glassmaking material becomes adherent, wherein, when 250 grams of the glassmaking material which is in free-flowing particulate form at room temperature is heated to said temperature, at which the glassmaking material becomes adherent, in a metal container made of the same material as the barrier, the material is to flow past and is held at said temperature for 30 minutes and the container is then inverted, at least 1% of the material adheres to the surface of the container, and wherein said temperature is the lowest temperature at which this condition is met. passing heated glassmaking material into a glassmelting furnace; combusting fuel with oxidant having an overall average oxygen content of at least 35 vol.% oxygen to produce heat for melting said heated glassmaking material in said glassmelting furnace and produce hot combustion products having a temperature greater than 982.2 °C (1800 °F); withdrawing said hot combustion products from said glassmelting furnace and feeding said hot combustion products into at least one first passageway of a heat exchange unit, wherein the temperature of said hot combustion products entering said at least one first passageway is at least 982.2 °C (1800 °F); flowing said hot combustion products through and out of said at least one first passageway; feeding glassmaking material into and through at least one second passageway of said heat exchange unit separated from said at least one first passageway by a barrier through which said glassmaking material and said hot combustion products cannot pass and through which heat from said hot combustion products passes to said glassmaking material to form said heated glassmaking material, with the at least one second passageway surrounding the at least one first passageway; and maintaining, by selecting the geometry of the first passageway(s), the total heat exchange surface area of the barrier and the distance of at least one inlet nozzle of the hot combustion products in the at least one first passageway from the barrier, the heat flux from hot combustion products in said at least one first passageway to said barrier sufficient that the temperature of the surface of said barrier that is in contact with said glassmaking material does not exceed 871.1 °C (1600 °F) and that the temperature of said glassmaking material does not reach or exceed the temperature at which the glassmaking material becomes adherent, wherein, when 250 grams of the glassmaking material which is in free-flowing particulate form at room temperature is heated to said temperature, at which the glassmaking material becomes adherent, in a metal container made of the same material as the barrier, the material is to flow past and is held at said temperature for 30 minutes and the container is then inverted, at least 1% of the material adheres to the surface of the container, and wherein said temperature is the lowest temperature at which this condition is met.