The difference is mainly syntactic. If "Zeit" is going to be specifically quantified in the post position, then the article induces parsing of a longer noun phrase
In der letzten Zeit, seit es nicht mehr regnet, ist es immer heißer geworden.
Whereas the sentence that implicitly defines the episode will be anchored on another key noun, with the tempus expressed in adverbial postposition. [I guess that's also why it should be a sentence in this paragraph.]
Die Hitze ist in letzter Zeit rasant gestiegen
But free word order renders the distinction mostly obsolete. The semantic overlap between time and weather (cf. season, day, tide, month etc.) adds to the ambiguity, as far as the indefinite "es" is concerned, The allusion is not actually lexically motivated, it's just that time is always symbolically derived from the observation of any process.
Although I do not assume a semantic distinction counciously, like the other answers as well. In addition I'd argue that a sentence starting with a proper subject will be virtually always followed by an indefinite article. e.g. "Ich habe in ..." "... letzter Zeit". Of course a fully qualified main clause can appear inserted, "Ich habe in der letzten Zeit [, in der es nicht geregnet hat, ] viel draußen unternommen". I am not deriving this from any formal framework and I'm surely not covering all use-cases. I'm just making a theoretical observation.
This syntagma is not limited to "Zeit", cp. e.g. "nächstes Mal" ~ "das nächste Mal"; "warmes Essen" ~ "das warme Essen". The difference seems to be in-/definite, cp. "ein letzt-e-s Mal" [encore], "ein warm-e-s Essen" (also "ein-e warm-e-_ Mahlzeit*). It should be obvious that a definitive das nächste Mal is nevertheless uncertain to a degree. The difference to the indefinite variant is as fuzzy as that between Konjunktiv or Future forms and the like, as far as expressions of Evidentiallity are concerned. Germanic is not exactly the prime example of an evidential language, that can--obviously--become qualified through adverbial gradiations, just for example.
PS: Insbesondere "insbesonder-e/s" shows that in was morphemic Also "indess".