Relative motion of the nucleus due to the temperature causes the Doppler effect broadening. But does the change of temperature also change the type of interaction, directly or indirectly? For example, since the temperature is higher, does it change qualitatively the probability of interaction for a given interaction? If so, how?
Doppler effect does not change the type of interaction .Energy variation on target nuclei changes the value of the interaction cross section , with different secondary effects .This effect is more important near resonance values of target nuclei cross sections .
A good example appears in light water reactors , Doppler effect acts on absorption cross section for uranium 238 . If water temperature increases , neutron absorptions increases in uranium 238 and the net power decreases : a good way for intrinsic security .
Probality of interaction between a particle and a isolated nucleus depend on the composition of the nucleus and the incident energy of the particle. In a gas made of isolated nucleuses, temperature modify the velocity spectrum of nucleus. This cause the relative velocity between particles and nucleus and so the probabilty of every incident energy to be modified, causing the Doppler effect. The nucleus does not have intrinsiquely a temperature and thus its properties are not modified by it.
If you now consider a gas made of molecules involving several nucleus, the answer is slightly different. Like for an isolated nucleus, temperature has a effect on the motion of the molecules. More, temperature has also a effect on the relative motion between nucleuses inside the molecule. This imply that the Doppler effect is different for a isolated nucleus or for a nucleus with molecular links with other nucleuses. For similar reasons Doppler effect is again different for nucleuses in solid materials. But in all cases it's still a question of relative velocity, not a dependancy of the nucleus properties on temperature.