It's true that the symbol "/ə/" is used to transcribe a range of sounds that includes sounds close to [ɪ], so there may is overlap between the range of vowel qualities used for "/ə/" and "/ɪ/". In particular, in American English, the "schwa" sound tends to be realized as a fairly "high"/"close" vowel that may sound similar to /ɪ/ or /ʊ/ when it is not word-final. In word-final position (as in the word "comma"), the "schwa" phoneme tends to be realized as a more open/low vowel that might be close phonetically to [ɐ] or [ʌ], so it might sound like the phoneme /ʌ/ or even /ɑ/. Here is a relevant chart from "The phonetics of schwa vowels", by Edward Flemming (2007) (I edited the copy on the right to circle the area covered by non-final schwa):
Another thing that may be causing confusion in the case of temerity is dialectal differences in the phonemic identity of reduced vowels. In some dialects, the pronunciation of temerity would standardly be transcribed as /tɪˈmɛɹɪti/: this is the pronunciation given by the OED, for example.
The identification of reduced /ɪ/ with /ə/ is known as the "weak vowel merger", and it tends to be a feature of American English (although it seems to exist in various degrees, not as a single yes-or-no sound change: the fact that you think of the pronunciation as being "/təˈmɛɹɪti/", with the first but not the second reduced vowel being identified with the schwa phoneme, seems like a good example of this).
Aside from its position in the word (final vs. non-final), another thing that influences the pronunciation of schwa is the surrounding sounds. The vowel in the first syllable of "temerity" occurs in the context "/t_ˈmɛɹ" while the vowel in the second-to-last syllable occurs in the context "ˈmɛɹ_ti". It may be relevant that the later vowel is right before a syllable containing the high vowel [i]. Flemming discusses the influence of surrounding sounds on the pronunciation of schwa, but I haven't spent enough time looking at the article to be able to summarize his findings.
"Moment" and other words traditionally transcribed with final /ənt/
In a standard accent without the "weak vowel merger" such as "RP" English, the word moment has /ə/, not /ɪ/, in the final syllable. But if you speak a dialect that does have the merger, you might hear the merged sound here as sounding like /ɪ/ because it is a non-final schwa.
Alternatively, the /n/ following the sound transcribed "/ə/" in this word might contribute to making it be pronounced in a way that you hear as "/ɪ/". It's well known that the sequence transcribed "/ən/" has a pretty wide range of possible phonetic realizations that vary between accents of English. E.g. some speakers, such as John Wells, report that there is a salient phonetic difference for them between a vowel-consonant realization [ən] and a syllabic consonant realization [n̩], and that these two pronunciations are distributed according to a fairly well-defined set of rules (my understanding is that according to Wells's rules, moment would have to be pronounced with [ən] and not [n̩], because the preceding nasal consonant /m/ is supposed to inhibit a syllabic nasal realization of /ən/). I myself find it difficult to notice any categorical difference between [ən] and [n̩] in my own speech; I don't know whether I actually consistently distinguish these variants in production according to some rule that I am unaware of.
I haven't yet found any linguistic sources that describe a tendency for any of the variant pronunciations of "ən" to be realized with phonetic [ɪ] or to be identified with the phoneme /ɪ/, but some speakers apparently at least perceive other speakers' pronunciations of (traditional) "ənt/n̩t" as involving some kind of front vowel:
see this blog post where an older speaker says that the pronunciation of student used by "the younger generation of [American English] speakers" sounds to him like it includes the vowel [ɛ]:
American English in the last decade or more has manifested a phonetic change whereby what was previously a syllabic /n/ in the clusters /dnt/ and /tnt/ at the end of words has instead developed an epenthetic [ɛ] preceding it. Accordingly, whereas the older normative pronunciation of words like student, hadn’t, didn’t, and patent typically had no vowel before [n], now the younger generation of speakers inserts an unstressed open mid-vowel [ɛ] before it.
("Desyllabication of /n/ in Consonant Clusters", Language Lore, by Michael Shapiro, 2015)
I am somewhat doubtful about Shapiro's identification of this vowel as the "open mid-vowel [ɛ]", and also, I don't think that this is an actual phonemic sound change involving the vowel phoneme /ɛ/. But it does seem to be at least a valuable piece of data about possible alternative perceptions of words that are traditionally transcribed as ending in /ənt/.
Similar perceptions are also brought up in the comments to the Language Log article "Ask Language Log: Trend in the pronunciation of Clinton?", by Mark Liberman (2016):
Ken Miner said,
July 30, 2016 @ 2:53 pm
I began to notice the [ǝn]/[ɪn] phenomenon in the 50s, when my then best friend, from Long Island, consistently pronounced ‘button’ [ˈbʌɾǝn]. Nowadays ‘didn’t’ as [ˈdɪɾɛnt] and so on I hear everywhere. Apparently not regional, but always from young people, I believe [...]
Steven Hartman Keiser said,
July 30, 2016 @ 8:11 pm
It was probably about 5 years ago that I first noticed this vowel variant in Midwestern speakers 20 years and younger (i.e., my own children), in words like "important" and "button".
The vowel sounds to me a bit closer to [ɪ] than [ə].
KarlG's answer to the ELU question "Pronunciation of boggling and similar *ing words" also suggests that some speakers use a front rather than a central unstressed vowel in the context _nt#, saying that there is a
tendency of some native speakers not to pronounce vocalic n in contractions such as didn't, wouldn't, or couldn't, instead inserting a schwa or lately even a fronted vowel before the n, or in words ending in -ant where vocalic n would otherwise be expected, like important. (Take that, Ezra Klein! See this video at 1:40 mark) While this particular pronunciation puts my teeth on edge, enough educated elites use it in their podcasts that calling it an error rather than a new variation seems ill-advised.
Another relevant Language Log post by Mark Liberman is "Clipping McDonald's" (2013), where he expresses skepticism of the idea that some dialects clearly distinguish different weak vowels in unstressed syllables (like /ɪ/ in Alice vs. /ə/ in Dallas).