Under what conditions, if any, is boreh nefashot said on hot coffee/tea?
If one is unsure if he drank "cheekfuls" is he exempt?
This is a big discussion among the halachic authorities. The Rivevos Ephraim 8:86 brings down that its a machlokes so he came up with an idea to take oneself out of the safek. He suggests after drinking the coffee he should drink a cup of water so he can definitely make a bracha achrona. Rav Chaim Shaul Eizenstaht told the Rivevos Ephraim that he heard from Rav Elyashiv the same idea.
The Shearim Metzuyanim Behalacha 51:6 with footnote on the Kitzur brings many shittos about this and discusses ice cream and sucking candies which have similar halachic considerations. He mentions shittas who hold one does make a bracha achrona. He also brings the idea of 8 minutes as achilas pras(Chasam Sofer) . The Maharam Shick was noheg to make a bracha achrona since on a regular basis one doesn't wait 8 minutes in between.
The Taz to Shulchan Aruch, Orach Chaim 210:1 writes regarding liquor that since it cannot be drunk as quickly as would be required for the normal shiur of beracha acharona on a drink, its shiur is at the standard of whatever people normally drink. This logic can be applied to hot drinks as well, and the Ba'er Heitev Shulchan Aruch, Orach Chaim 204:12 cites many authorities who say as much regarding coffee.
The Ba'er Heitev there concludes that the accepted practice is not to say a blessing, and the best thing to do is to leave a bit to cool down and drink quickly at the end.
I heard from a posek in Baltimore that R' Elyashiv held that even if you let it cool down you still would not make a beracha acharona, because it is not the normal way to drink hot coffee cold. (I don't know how to distinguish between cold hot-coffee and ice-coffee, but I assume it follows the intention of the drinker and/or how it was served.) So according to R' Elyashiv, you never make a boreh nefashos after drinking a hot drink.
As always, CYLOR.
The Kitzur Shulchan Aruch in סימן נא - כללים בברכה אחרונה says:
סעיף ו': שָׁתָה מַשְׁקֶה חַם בִּמְעַט מְעַט, (כְּגוֹן טֵה אוֹ קַאפֶע), כֵּיוָן שֶׁאֵינוֹ שׁוֹתֶה בְּפַעַם אַחַת כַּשִּׁעוּר, אַף עַל פִּי שֶׁדֶּרֶךְ שְׁתִיָּתוֹ בְּכָךְ, מִכָּל מָקוֹם אֵין מִצְטָרְפִין וְאֵינוֹ מְבָרֵךְ בְּרָכָה אַחֲרוֹנָה (ר"י).
If you drink anything hot in small sips - even if that's the way everybody drinks it - since you didn,t drink a shiur (the required amount for an after Bracha) you do not make Boreh Nefashot.
So how much is this shiur? This he answers a few lines earlier in סעיף ב:
וְעַל מַשְׁקִין, יֵשׁ אוֹמְרִים, דְּאֵינוֹ חַיָּב בִּבְרָכָה אַחֲרוֹנָה אֶלָּא אִם כֵּן שָׁתָה רְבִיעִית. וְיֵשׁ אוֹמְרִים, דְּגַם עַל מַשְׁקִין אִם שָׁתָה כַּזַּיִת, חַיָּב בִּבְרָכָה אַחֲרוֹנָה, וְלָכֵן לָצֵאת מִידֵי סְפֵקָא, יֵשׁ לִזָּהֵר שֶׁלֹּא לִשְׁתּוֹת אֶלָּא פָּחוֹת מִכַּזַּיִת אוֹ רְבִיעִית. וְאֵין חִלּוּק בֵּין יַיִן שָׂרָף לִשְׁאָר מַשְׁקִין (ק"צ ר"י)
There's an unresolved dispute as to whether the shiur for Boreh Nefashot on beverages is a Revi'is (about 86 cc) or a Kzayit (the size of an olive).
As a result, one should be careful to [always] drink less than a Kezayit or to drink [at least one gulp] more than a Revi'is.
When in doubt? The Halacha is that if one is unsure if one needs to say a Bracha, then one does not say it.
So to answer your questions:
Under what conditions if any is boreh nefashot said on hot coffee/tea?
If one drank at least 86 cc consecutively. That's about 2 cheekfuls.
If one is unsure if he drank "cheekfuls" is he exempt?
Yes, but one should - preferably - drink less than an olive-size per sip.