XRF is "non-destructive," but what actually happens to the sample?
The title of the question is about sample heating by ED-XRF instrument. Yet, OP is wondering its limitations and like to understand what kind of compounds analysts might lose to some sample heating if they switch to ED-XRFs (bench-top?). I hope this may be addressed by MaxW, when OP has said whay kind of samples they are analyzing. However, general knowledge on these instruments would predict both WD- and ED-XRF instruments would heat samples regardless of what kind of instrument is in use, but I'd suggest ED-XRF would heat less than that of WD-XRFs since they are low energy instruments.

Actually, to me, the bigger question is which kind is more sensitive to particular elemental analysis, regardless of sample kind (e.g., environmental or archaeological). My literature survey on the subject indicate that ED-XRF instruments is more qualitative than quantitative toward analysis, specifically towards analysis on low-$Z$ and medium-$Z$ elements (References 1 &amp; 2).

The authors of ref.2 pointed out that the energy dispersive X-ray fluorescence analysis of low-Z-elements can generally be seen as a challenge. They have adjusted the instrument in several ways to get better data. The abstract of the article has well reflected the point:


  Photoninduced energy dispersive X-ray fluorescence analysis in total reflection geometry has been applied to low-$Z$ elements. To avoid the absorption in the $\ce{Be}$-window a windowless $\ce{Si(Li)}$-detector has been used. Icing of the detector crystal is prevented by a thin $\ce{C}$-foil. Physical reasons of the low energy background are reduced using a high energy cut-off reflector. Measurements of low-$Z$ elements from $\ce{O}$ ($Z= 8$) onwards are possible and detection limits in the $\pu{ng}$ region are obtained.


Anybody interested in these adjustments should get the article, which has explained them with some depicted diagrams.

On low-$Z$ element analysis, authors of Ref.2 claimed that:


  WD-XRF is the best XRF approach for measuring and quantifying low-$Z$ elements. ED-XRF spectrometers are subject to limitations, such as Bremsstrahlung radiation and escape peaks, which affect detection and quantification of low-$Z$ elements in particular. Although we will demonstrate in Section 2.3 that, under the right conditions, pXRF spectrometers can simulate the performance of bench-top ED-XRF instruments, there are two notable exceptions: $\ce{P}$ and $\ce{Na}$ (Note: the notation pXRF spectrometers are for portable-ED-XRFs).


The following diagram from Ref.2 well explained point, which shows exceptional correlation ($R^2=0.995$) of expected to measured concentrations of $\ce{P2O5}$ when WD-XRF is used:



References:


Alice M. W. Hunt, Robert J. Speakman, “Portable XRF analysis of archaeological sediments and ceramics,” Journal of Archaeological Science 2015, 53, 626-638 (https://doi.org/10.1016/j.jas.2014.11.031).
C. Streli, H. Aiginoer, P. Wobrauschek, “Total reflection X-ray fluorescence analysis of low-Z elements,” Spectrochimica Acta Part B: Atomic Spectroscopy 1989, 44(5), 491-497 (https://doi.org/10.1016/0584-8547(89)80055-2).