Yes, that also involves tunneling.
not nuclear fusion at room temperature.
You are mistaken; nuclear fusion does indeed occur at room temperature, just at a very low rate (if you were assuming a zero probability because of the "semiclassical method" in the article to which you linked, bear in mind that it approaches zero only at higher scales, but never actually reaches zero, and is very much non-zero at quantum scales).
Those who denounced Pons and Fleischmann regarding their cold fusion (now known as LENR) are starting to realize they have egg on their face. It is increasingly clear that despite having made mistakes (which is true in all experiments) that their apparatus DID manage to fuse nuclei. No one yet has been able to explain why or how they managed to get such a remarkable result, but is clear that many similar experiments are fusing nuclei.
Excess energy DOES appear to be released. Fusion actually APPEARS to be occurring. Efficient use of this energy requires that experiment and theoreticians uncover the mechanism and principles underlying the process, and to increase the number of reactions many orders of magnitude. One of the runs of Pons and Fleischmann seemed close to the magnitude needed, but it has not yet been able to be replicated. The current experiments are using very closely controlled parameters for good reason, and they have not strayed into whatever “perfect error” that P&F quite possibly made. I won’t be surprised if Pons and Fleischmann eventually get a Nobel Prize for their widely derided work.
I remind everyone that it has been common in the history of science that well known phenomena have not been properly explained by the theoreticians for hundreds of years.