Michael,

I understand you are trying to cross run (hot tap) on to a hot above ground piping which you call it header.

I think there is no short-cut for estimating header thermal displacement and the effect of new piping attachment. If you are lucky you can find an anchor support close to the attachment location and pipe guided against lateral movement, lateral rotation under thermal load. Otherwise you should model up to the thermal neutral location on the header to be able to answer future questions which may arise.

Main header will be hot under the operating temperature, the new piping will be cold. So you may be forced to see the effect off the shut down of combined piping in case the temperature significant(?).

I know this was not the answer you were not expecting. However it may help you rethink.