The biggest thing to keep in mind is that your load cases become more complicated.

You are going to need to know where the existing piping is anchored (which you would always want anyway when making a connection to existing piping). In your modeling, you are going to need a "normal" case where the existing piping doesn't "heat up" as it is already in position and won't grow more (maybe). The new pipe will heat up. From this standpoint, your tie-in is effectively an anchor point. You need to make sure that the new pipe has enough flexibility on its own as there will be no balancing from the existing header.

Then, it gets worse! You need to build another case, this time, the new pipe needs to be set "ambient", and the existing pipe will need to be coded to contract back to it's installed position. Hot Tap arrangement are where I find myself going for direct coding of the alpha value instead of the temperature (you then will also directly code the allowable stress value).

Finally, you need to take the difference between those two cases in order to see what the full displacement stress range is.

Actually, your case looks to be even more complicated as you're not making just one tie in, but putting in a whole new bypass connecting to the main line in two places. Hopefully the two connections are fairly close together, as that will help you.

I guess my main point is that you need to sketch out and understand what the various temperature cases can been in each line and make sure you account for them in the model.