Benjamin Olson
Hero
I think you generally make a more viable and less one note character if your interpretation of thematic specializing is "I will favor this thing and eschew this thing, and that thing, and the other thing", rather than "I will only ever use on brand spells and abilities".
For example, while I would expect a pyromancer to take a lot of fire spells, and not invest in other elemental damages, that doesn't mean they could not learn all manner of non-elemental evocation related spells and be able to do other things. Pyromania can just be one important aspect of their repertoire, rather than the be-all-end-all of it. As for learning cone of cold, I would say only if you are ruling at your table that that spell puts out fires, in which case having an off-button spell or two is very on-brand to being able to control fire.
For example, while I would expect a pyromancer to take a lot of fire spells, and not invest in other elemental damages, that doesn't mean they could not learn all manner of non-elemental evocation related spells and be able to do other things. Pyromania can just be one important aspect of their repertoire, rather than the be-all-end-all of it. As for learning cone of cold, I would say only if you are ruling at your table that that spell puts out fires, in which case having an off-button spell or two is very on-brand to being able to control fire.