Thats a design question and not likely to find an answer here or in any other forum for that matter.
What's the pressure?
What's the amplitude of the pressure variation in the cycle?
What's the max temp?
What's the min temp?
What's the rapidity with which the temp amplitude changes?
What's the cycling frequency?
What alloys?
What's the service-is it a SCC susceptible?
What's the material thickness?
Are there any thickness transitions?
What about weld quality?
What was the welding thermal cycle-did it prevent segregation?
Etc. etc. etc.

Although the effects of thermal expansion coefficient of the materials involved is usually related to design conditions and the effects on the weldment in service as mentioned earlier, the only practical problem I see when doing the welding, is the restraint that might be applied across the joint during the heating and cooling cycle of welding. This might lead to cracking as Giovanni has indicated.

If the weld is between two freely moving pieces, then although they both heat up along with the filler, when they cool, because they are unrestrained no detriment should occur in the weld (cracking may still take place due to compositional reasons but this is not what we are concerned with here). If the weld is a closing weld, then the expansion of the parent due to heating may close gaps and on cooling more residual stress might be locked into the joint.  Cracks might now occur if the restraint is sufficiently higher than in the unrestrained weld. Resudial stresses would also be introduced into the weld and parent - these would be present anyway, but the higher the thermal coefficient of expansion the more the magnitude of the residual stresses. Is this correct?

I agree however that in practical terms, the values quoted are more or less similar and no problems should be anticipated.

I don't mean to be disrespectful, but I must have missed something? I don't recollect suggesting fatigue testing. I only noted that low cycle thermal fatigue can be an issue if the operating conditions or service conditions involve thermal cycling.

A case in point: I have a client that welded carbon steel to 304 stainless steel to fabricate an apron used in the opening of a large heat treating oven. The concern was that the forklifts were continually bumping into the refractory and crushing it. So the carbon steel apron was to provide a barrier against the fork trucks and the stainless steel was to resist the high temperatures of the oven and the occasional bump of a hot piece dropped on to the refractory. They called me in when the new fabrication tore itself apart in the matter of weeks.

The carbon steel and 304 austenitic stainless steel have definite differences in thermal coefficients of expansion. I believe the difference was substantial enough that low cycle thermal fatigue was the culprit. Every time the oven door was opened, a rush of cold air would cool the stainless steel, upon closing the door, it would be reheated to a high temperature. The thermal cycles were repeated several times per shift, three shifts per day. As I said, the apron failed in short order without apparent impact damage from the forklifts. In the absence of physical damage, I assumed the failure was the result of the thermal cycles.

A new apron was designed with some "slip joints" between the hot section and the cold section. It has been in operation for more than a year without signs of failure. 

If thermal cycling isn't a consideration, then low cycle thermal fatigue isn't an issue. Austenitic stainless steel typically has sufficient ductility to accommodate considerable differences in expansion and contraction if the only thermal cycle involved is that of making the weld.

Best regards - Al