Published in the i newspaper on 24 October 2020.
Having wisely decided to avoid the last two Inquisitors, I was pleased to find one that I could complete without too much difficulty. There was a slight ambiguity in the preamble but fortunately I guessed the correct interpretation and didn't need too many outside hints. I was bit late cottoning on to the theme, though - about halfway through I had __OV_L_ES_ALE in the right-hand extra column, and could only think of TWO-VALUE SCALE (corresponding with the "hot and cold" of the title). I was looking for similar pairs of opposites in the grid and couldn't see any! Once I got the correct answer, most of the puzzle fell into place.
The preamble said "one letter per grid row is not indicated by the wordplay of the clues". It was important to realize that the restriction could affect Down as well as Across clues; for instance, the E at row 13, column 9 is part of 54 across but also part of 43 down, so it was omitted from the wordplay for both clues. This wasn't made explicit but I think careful reading of the preamble made it clear. The Down clues affected were 8 down (V in row 4), 2 down (I in row 5), 11 down (L in row 6), 35 down (E in row 8), 9 down (S in row 9), 48 down (L in row 12) and 43 down (E in row 13).
However, what wasn't completely clear from the wording above was whether all occurrences of a given letter in each row were to be treated similarly. For instance, were the E's at row 13, columns 5 and 12 also omitted from the wordplay of the clues? It turned out that they weren't, but I think the wording could have been made less ambiguous.
The right-hand "thematic entity" was in fact SCOVILLE SCALE - the scale traditionally used to measure the hotness of chili peppers. This led almost immediately to the "general" term CAPSAICIN in the top row - the substance that gives chili peppers their hotness - and then to seven specific types of pepper: CAROLINA REAPER in row 2, NAGA VIPER in row 4, SCOTCH BONNET in row 6, JALAPENO in row 8, ANAHEIM in row 10, PIMENTO in row 12 and BELL PEPPER in row 13. They were arranged in descending order of hotness, down the grid; very neat!
Detailed solutions follow, with letters omitted from wordplay indicated by underlining. There were quite a few clues I couldn't parse.
Across
1. ICECAPS = "frozen mountain peaks"; I + (C in rev. of PACE)
7. ICING = "coating"; ?
12. CAROLINA = "former British colony", etc.; A + ROL[e] + IN + A
13. REAPER = "death"; [e]PE[e] in REAR
14. IN HOLES = "full of cavities"; INHALES - A (A is the former chemical symbol for argon)
16. MRSA = "highly resistant bacterium"; MRS + A
19. TUTENAG = "zinc"; (TE in TUN) + AG
20. VIPER = "snake"; ?
21. OINK = "noise made by sucker, perhaps"; [conma]N in OK ("sucker" ref. to pigs?)
23. MHO = "former unit of resistance"; hidden in [hel]MHO[ltz]
25. MATE = "ship's officer"; ?
26. SCOTCH = "put an end to"; SCOT + CH
29. BONNE = "French maid"; [apro]N in BONE (="bobbin", why?)
32. TEL = "hill in Arabia"; T[roglodyt]E
33. TOIL = "great difficulty"; TO + I
34. CERISE = "purplish-red"; C + [ros]E + RISE (C = "see", homophone)
37. JALAP = "purgative root"; A in (J + LAP) (J = "joint"?)
39. NOTE = "set to music"; N + OT
40. CRED = "ability to inspire belief"; CREE - E + D (why D = "God's"?)
42. CIMAR = "shift"; (rev. of M1) in CAR, with I = 1
45. SEAS = "great waves"; EAS[e]
46. RACE = "stock"; RAGE - G
47. ANAHEIM = "where one might see Pluto"; AN + (HE in AIM) (AIM = "place"?)
Note: Anaheim, Florida is the location of Disneyland.
49. BENNUT = "oil-producing seed"; B + rev. of TUNNE[l]
50. ANOESIS = "sensation that's not understood"; anag. of NOISES
51. PIMENT = "vintage spiced wine"; anag. of PITMEN
52. OVERFLEW = "soared higher"; (HOVER - H) + FEW
53. NOBEL = "Swedish chemist"; OBE in NL ( = non licet, "it is not permitted")
54. PEPPERY = "irritable"; (rev. of EPP) in PRY ( = "peer")
Down
2. CANTICO = "dancing-match"; CANT + CO
3. ERHU = "Chinese instrument that's bowed"; middle of [ov]ERHU[ng]
4. ALLEY = "back lane"; rev. of (YELL + A) (is a YELL "something very funny"?)
5. PIEND = "outward-pointing angle"; PI + END (PI = "confusion"?)
6. AARGH = "cry of anguish"; AAR + GH
7. IRMA = "German girl"; IR + MA ("Irma" is originally a German name)
8. CERVINE = "fawn-coloured"; anag. of (CATHERINE - HAT)
Note: Def. is "relating to deer", and a fawn is a young deer - part-cryptic definition?
9. IASI = "Romanian city"; I + AS + I (Swedish ås = "ridge of gravel"?)
10. GENET = "fur"(?); ?
Note: A genet is a slender cat-like animal. I don't understand this clue at all.
11. PRERELEASES = "previews"; anag. of (SEES + REAPER) (solution to 13ac)
15. SAMBA = "syncopated dance"; S (="past"??) + (rev. of MA) + BA (="Highland ball"??)
Note: Very unsure about this.
17. APATITE = "calcium-based mineral"; (A TIT) in APE
18. POSTSCRIPT = "supplementary"; P + anag. of SCOTS + RIPT ("previously" = archaic?)
22. NOISE = "sound"; homophone of "noys" (dialect word for "annoys")
24. ONCE = "former"; C in ONE (= "drink", as in "do you want one?")
27. CHACONNE = "old Spanish dance"; anag. of NO CHANCE
28. HALIBUT = "fish"; BUT ( = "barrel"?) beneath ( = "propping up") HAL I
Note: Either BUT is an alternative spelling of "butt", or it's a reversal of TUB with "up" as the reversal indicator somehow detached, in which case beneath = "propping".
30. OUPA = "old man in Cape Town"; O + UP + A
Note: South African term of address for a grandfather or elderly man.
31. EROS = "asteroid"; rev. of ORE (="mineral source")
35. SEAMIER = "more disreputable"; anag. of ARMIES
36. ARABIN = "source of gum"; RABI (="Indian grain harvest") in AN
38. AMATOL = "high explosive"; (AMATI - I) + O + L
41. DENEB = "star"; D + EN + rev. of (PROBE - PRO) (PRO = "for". Tricky!)
43. RANEE = "Indian queen"; RAN + E
44. THORP = "hamlet"; first letters of T[ragedy], H[...], O[...], R[...], P[rince]
48. ISLE = "key"; E below IS
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