The inside wall is also not at the 6000°C that you have in the center of the combustion chamber. There is a bit of film cooling taking place by injecting hydrogen-rich gas at the sides of the combustion chamber without also injecting oxygen into the stream, also the exhaust cools a bit while expanding in the noozle.
I have some simulation data here, it is not 100% accurate, but gives you a good impression of the conditions at the nozzle heat exchanger:
Variable
|
Description
|
Units
|
65% RPL
|
100% RPL
|
104% RPL
|
109% RPL
t_4|Fuel temp. inside nozzle HE|R|449.5|465.8|456.4|448.1
t_5|Fuel temp. inside MCC HE|R|509.0|466.0|455.9|443.1
t_9|Preburners fuel supply line temp.|R|295.4|276.4|276.4|276.5
t_op|Oxidizer preburner temperature|R|1,057.0|1,440.3|1,475.8|1,517.6
t_fp|Fuel preburner temperature|R|1,633.5|1,753.9|1,796.1|1,854.8
t_fi|Fuel injector temperature|R|1,392.7|1,560.7|1,593.1|1,636.2
t_c|Main chamber (MCC) temperature|R|6,400.0|6,400.0|6,400.0|6,400.0
tw_15|Hot wall temp. at MCC HE|R|1,228.8|1,214.9|1,203.1|1,187.1
tw_25|Cold wall temp. at MCC HE|R|509.0|466.0|455.9|443.1
tw_14|Hot wall temp. at nozzle HE|R|1,162.5|1,260.3|1,250.4|1,244.5
tw_24|Cold wall temp. at nozzle HE|R|449.5|465.8|456.4|448.1
In case Rankin aren't that easily understood... I can also convert the data into K or °C, the original table was calculated in Rankin