Cognate with Saterland Frisian Dai (“day”), West Frisian dei (“day”), Dutch dag (“day”), German Low German Dag (“day”), Alemannic German Däi (“day”), German Tag (“day”), Swedish, Norwegian and Danish dag (“day”), Icelandic dagur (“day”). Cognate also with Albanian djeg (“to burn”), Lithuanian degti (“to burn”), Tocharian A tsäk-, Russian жечь (žečʹ, “to burn”) from *degti, дёготь (djógotʹ, “tar, pitch”), Sanskrit दाह (dāhá, “heat”), दहति (dáhati, “to burn”), Latin foveō (“to warm, keep warm, incubate”).
The standard reconstruction identified three coronal/dental stops: */t/, */d/, */dʰ/. They are symbolically grouped with the cover symbol T. In so-called "thorn clusters" of the form TK in all branches except Anatolian and Tocharian a metathesis occurred, resulting in dorsal-coronal clusters of non-obvious phonetic makeup. **Metathetized and unmetathetized forms survive in different ablaut grades of the root *dʰégʷʰ "burn" (whence also English day) in Sanskrit, dáhati "is being burnt" < dʰégʷʰ-e- and kṣā́yat "burns" < dʰgʷʰ-éh₁-. See the section on PIE phonological rules, below, for more discussion and examples.
I doubt this etymology just because I can't find any reference of this kind of saying that *PIE dʰegʰ- "day" and *dʰegʷʰ- "burn" are cognates.
PS: the reconstructions are based on here, in footnote 8 on page 2 of which the author even deny this connection and E. day comes from *PIE dʰegʰ- "to repeat itself (over and over again); cycle".