Instead of matching or exceeding the Flamelock's temperature, drain it. Siphon heat from the firewall itself. Cool it down from 47,239°C to something survivable. You become the entropy sink. The firewall cools. You walk through the cold gap.
Thermodynamics problem: Second Law. Heat flows from hot to cold, not the other way. To actively siphon heat FROM the Flamelock, you need a heat pump operating across a 47,202°C gradient. The Carnot efficiency of such a pump: η_carnot = 1 - T_cold/T_hot = 1 - 310/47512 = 99.35%... reversed, meaning you need to input an enormous amount of work.
Required power: 4 solar luminosities. Your available power: 80 watts. The ratio is not in your favour by a factor of 5×10²⁴. This is the same order of magnitude as the number of atoms in your body. In case the universe is sending a message.
Siphon attempt: draining at maximum biological rate (80W heat extraction). Target: 10²⁵ W total heat budget.
Drain progress: 0.000000000000000000000000%
Estimated time to cool Flamelock by 1°C: ~3.96×10²³ years (27× the current age of the universe)