The only free and comprehensive online etymological dictionary of the Spanish language
frío m. (Adjective, Noun) "cold"

10th cent. Old Spanish frido. From Latin frigidus 'id.,' from the verb frigere "to be cold." Ultimately from frigus "cold." From Proto-Italic *srīgos- 'id.' From Proto-Indo-European *sri̯Hǵ-os- 'id.'

Also the origin of Frías, the name of a town in Burgos and another in Teruel.

Romance: Western Vulgar Latin: Asturian fríu, Portuguese frio, Galician frío, Catalan fred, French froid, Italian freddo

Indo-European: Hellenic: Ancient Greek ῥῖγος (rhîgos) "cold," "frost"
fruir (Verb) "to enjoy"

From Latin frui 'id.' From Proto-Italic *frūg-je/o- 'id.' From Proto-Indo-European *bhru̯g-i̯e/o- "to use."

Romance: Western Vulgar Latin: Portuguese fruir, Catalan fruir, Italian fruire
fruta f. (Noun) "(a piece of) fruit"

13th cent. From fruto.

Romance: Western Vulgar Latin: Asturian fruta, Portuguese fruta, Galician fruita, Catalan fruita, French fruit, Italian frutta
fruto m. (Noun) "fruit"

10th cent. From Latin fructus "enjoyment;" "fruit," derived from earlier frui "to enjoy" (see fruir).

Romance: Western Vulgar Latin: Asturian frutu, Portuguese fruto, Galician froito, Catalan fruit, French fruit, Italian frutto ; Eastern Vulgar Latin: Eastern Vulgar Latin: Aromanian frut, Romanian frupt ; Sardinian: frutu

Italic: Umbrian frif "fruits," Oscan fruktatiuf "usufruct"

Indo-European: Germanic: Gothic brukjan "to use," Old High German bruhhan 'id.,' Old Saxon brukan 'id.,' Old English brucan 'id.'

"The restriction to Gm. and It., and the pervading zero grade, may cast doubts on a PIE origin; yet there is no decisive argument against it." ~ M. de Vaan, Etymological Dictionary of Latin (2014)
fuego m. (Noun) "fire"

12th cent. From Late Latin focus 'id.,' from Latin focus "hearth." Of unknown origin.

Also the origin of the surnames Fuego, Fuejo and Fogón, originally given as a nickname to high-spirited individuals.

Romance: Western Vulgar Latin: Asturian fueu, Portuguese fogo, Galician fogo, Catalan foc, French feu, Italian fuoco; Eastern Vulgar Latin: Aromanian foc, Romanian foc; Sardinian fogu
fuente m. (Noun) "source;" "fount"

10th cent. From Latin fontem, accusative of fons "fountain." From Proto-Italic *fonti- "(water) spring." From Proto-Indo-European *dhonh2-ti̯- 'id.' From the root *dhenh2- "to flow."

Romance: Western Vulgar Latin: Asturian fonte, Portuguese fonte, Galician fonte, Catalan font, French fonts, Italian fonte

Indo-European: Indo-Iranian: Sanskrit dhani "to flow;" Tocharian: A tsnāntär "to flow," B tsnamo "flowing"
fuera (Adverb) "outside"

10th cent. Old Spanish fueras; 12th cent. fuera. From Latin foras 'id.' From Proto-Italic *forā- "to the door," accusative case of Proto-Indo-European *dhu̯ō̆r-h2- "doors" in either the dual or as an ancient plurale tantum (see note under -a).

Romance: Western Vulgar Latin: Portuguese fora, Galician fóra, Catalan fora, Italian fuori; Eastern Vulgar Latin: Aromanian fãrã, Romanian fără

Indo-European: Celtic: Old Irish dorus, Old Welsh dor, Middel Breton dor, Cornish dor; Germanic: Gothic daur, Old Norse dyrr, Old High German turi, Old Saxon dor, Old English dor (English door); Balto-Slavic: Old Church Slavonic dvьrь, Lithuanian dùrys; Albanian: derë; Hellenic: Ancient Greek θυρᾱ (thura), Mycenaean *tu-ra-; Armenian: dowr-k'; Indo-Iranian: Sanskrit dvā́r-, Young Avestan duuar-; Tocharian: B twere; Anatolian: Hittite andurza "indoors"
fuero m. (Noun) "historic law;" "jurisdiction"

10th cent. From Latin forum "forum." From Proto-Italic *fworo- "vestibule." From Proto-Indo-European *dhu̯or-o- "door." Probably developing in a sense of a room with doors becoming a public venue.

Romance: Western Vulgar Latin: Portuguese foro, Catalan forum, French for, Italian foro; Eastern Vulgar Latin: Romanian for

Italic: Umbrian furu

Indo-European: Celtic: Gaulish Augusto-durum (Roman name for the city of Bayeux) "Augustine's forum;" Balto-Slavic: Old Church Slavonic dvorъ "court," Lithuanian dvãras 'id.;' Indo-Iranian: Sanskrit dvāram "passage"
fuerte m. (Adjective, Noun, Adverb) "strong;" "fort;" "loudly"

As an adjective first attested in the 10th cent; as a noun, 16th cent. From Latin fortis "strong." From Proto-Italic *forkt-i/o- 'id.' From either *bhorg-to-, *dhorg-to-, or *gwhork-to- 'id.' in Proto-Indo-European, with three possible ancestral consonants.

Romance: Western Vulgar Latin: Asturian fuerte, Portuguese forte, Galician fuerte, Catalan fort, French fort, Italian forte; Eastern Vulgar Latin: Romanian foarte

Italic: Oscan fortis

Indo-European: Celtic: Gaulish -briga "hill," Old Irish brí 'id.,' Middle Welsh bre 'id.,' Middle Breton bre 'id.,' Cornish bre; Germanic: Gothic bairgahei "mountainous," Old Norse bjarg "mountain," Old High German berg 'id.,' Old Saxon berg 'id.,' Old English beorg 'id.' (English barrow); Balto-Slavic: Lithuanian dir̃žti "to harden," Latvian derža? "whip" (uncertain etymology); Armenian: barjr "high;" Indo-Iranian: Sanskrit barh- "to make strong," Young Avestan barəzah- "height;" Tocharian: A pärkär "long;" Anatolian: Hittite parku- "high"
fuerza f. (Noun) "force"

Early 12th cent. From Late Latin fortia 'id.,' the neuter plural of fortis "strong" (see fuerte for further etymology).

Romance: Western Vulgar Latin: Asturian fuerte, Portuguese forte, Galician fuerte, Catalan fort, French fort, Italian forte; Eastern Vulgar Latin: Romanian foarte