The question is a little broad and as VPL states the end user should generally specify the design temperatures. However, because there is some doubt in my mind as to what your question is really asking. I have provided you with three answers that do overlap a little.
A shell and tube heat exchanger has two sides, namely shell and tube, and therefore two design temperatures.
Anything that is in contact with the tube side shall be designed to the tube side temperature. Anything that is contact with the shell fluid side shall be designed to the shell side temperature. Some items are in contact with both shell side and tube side fluids shall be designed for the hotest (and coldest) design temperatures. These items include tubes and tubesheet. Think about what temperature a item could get up to if shell side fluid stops and then if the tube side fluid stops, that should help you.
Alternatively, you may be asking the question - how do you calculate the tube and shell temperature to enable to work out the expansion in different scenarios. This needs to direction from the purchaser, they are the ones who know the impact of failures eg say cooling water failure. Specific items to consider are start up, loss of fluid on one side etc.
Thirdly, are you asking about items of a shell and tube heat exchanger need to be designed for elevated temperature to ASME? Answer anything that retains pressure - therefore you do not need to design the baffles, impingement plates, tie rods, spacers etc. However you do need to consider the material suiability at the temperatures they will encounter.