Canonfire! has a good Bullywug article with an extensive bibliography that should list all the early-D&D sources of info on bullywugs.
More recently, Pathfinder has renamed the bullywug the "boggard" due to IP concerns and has used them extensively, see this wiki article and its references but especially the "Ecology of the Boggard" in the Kingmaker adventure path. All this information has the virtue of being in print and easily obtainable, though any crunch will be 3.5 compatible and not 4e compatible.
All mentions, that I am aware of, regarding Bladesingers are below:
Bladesingers are mentioned in the edition after AD&D 2nd Edition, and despite its contradiction to 'guilds' or 'schools' there is no mention of any particular weapon (besides blades) to be in use.
What that means, in that edition, is a school representing animals went to the way side. in the revised edition, D&D 3.5 Edition, Bladesingers were mentioned as well.
It is essentially a copy paste, with a lot omitted, from Races of Faerun. Only "swordplay" and "any martial weapon" is mentioned. Nothing about schools guilds at all. There is another book the Bladesinger is mentioned, but its essentially only a blurb.
Once again, only sword is mentioned; probably due to racial sword proficiency - and the implication of blade in the name Bladesinger. Eventually, near the end of this edition, Bladesingers became Duskblades, and lost its 'elf-only' motif.
No mention of guilds or schools, or even preferred weapons were mentioned. Any martial weapon it appeared to be - but spending a feat to use a whip...most people would say, "no thank you." Bladesingers were included in the edition after this one, much to my surprise. But, it discredits the 'different weapons' aspect entirely.
Now we come to D&D 5th Edition, and you already have the published information on them thus far. Since, to my knowledge, that edition is to harken back to the days of simpler game-play and more intrinsic role-play; rather than the vice versa, take this opportunity to "Create Your Own" schools, guilds, and organizations.
Best Answer
There's (potentially) a lore-backed mineral that generates heat right in the 5e PHB.
The Trinkets table, p. 151 of the Fifth Edition PHB, contains a reference to the following:
Because trinkets are supposed to be mysterious oddities and potential adventure hooks, there is no narrative explanation provided for why the shard of obsidian generates heat. The very appearance of the shard on the Trinkets table arguably implies that it is special in some way, and that its heat-generating quality is unusual. (Ordinary, real-world obsidian doesn't meaningfully generate heat, after all.) It could be, for example, that something has been done to this specific shard to cause it to generate heat. But it could just as easily be that all obsidian in your game's setting generates heat -- although that might diminish the uniqueness of this particular trinket. For that matter, the fact that it "feels warm" could arise from something other than actual warmth -- an illusory feeling in the mind of the person touching the shard, for example.
In any event, if you're looking for precedent, there it is.
There are other (potential) options from the 3e Forgotten Realms supplement Magic of Faerûn.
MoF includes numerous "special materials" that can be used to craft items. A couple of those materials, if used to create weapons, provide bonus fire damage: fever iron, a magic metal from volcanic craters (p. 178), and hizagkuur, a magic metal from the Underdark (p. 179).
Curiously, neither entry explicitly says the materials feel warm or otherwise generate heat in any way except dealing fire damage. Nevertheless, it stands to reason that a substance that deals fire damage would have to generate heat somehow -- on impact at the very least.