jmdict 2725580 Active (id#2333450)
涼しげ； 涼し気 [rK]
【 すずしげ 】
  1. [adj-na]
    • cool (of temperature)
    • refreshing
    Cross references:
    • ⇒ see: 1554370 涼しい 1. cool; refreshing
  2. [adj-na]
    • clear (of sound, objects, etc.)
    • bright
    Cross references:
    • ⇒ see: 1554370 涼しい 2. clear (e.g. eyes); bright
  3. [adj-na]
    • composed
    • calm (demeanour)
    • cool
    • unruffled
    Cross references:
    • ⇒ see: 1554370 涼しい 4. composed (facial expression); unruffled; unconcerned
History:
    • A 2025-02-28 03:29:36 Jim Breen (id#2333450)
    • Comments
      Thanks; it needed work.
    • A* 2025-02-27 09:11:16 Sombrero1 (id#2333421)
    • Comments
      I think "refreshing to look at" doesn't cut it. Maybe something like this?
    • Refs
      Google N-gram Corpus Counts
╭─ーーー─┬───────────┬───────╮
│ 涼しげ │ 1.069.854 │ 98.4% │
│ 涼し気 │    16.970 │  1.6% │[rK]
╰─ーーー─┴───────────┴───────╯

I think the glosses are a bit odd. I think there's more than one sense here

https://massif.la/ja/search?q=涼しげ

Many sentences using a construction like this: いつも通り、涼しげな顔をしている。(composed expression), which doesn't refer to temperature. 
But likewise there's sentences with "涼しげな風" (refreshing breeze) and "涼しげな音" (clear sound) etc.

Some more sentences from massif and reverso:
鈴虫が鳴くような、涼しげな音色が耳に触れる。(clear sound)
奥には滝があり、その周辺の少し涼しげな空気がとても気持ち良いです。(refreshing/cool atmosphere)
涼しげなガラスの器に盛りつけられた野菜たちが、　キラキラと輝いています。 (clear glass)
すると、彼女は涼しげに解説してくれた。(explained calmly/in a composed manner)

.
    • Diff
      @@ -8,0 +9 @@
+<ke_inf>&rK;</ke_inf>
@@ -14,0 +16,15 @@
+<xref type="see" seq="1554370">涼しい・1</xref>
+<gloss>cool (of temperature)</gloss>
+<gloss>refreshing</gloss>
+</sense>
+<sense>
+<pos>&adj-na;</pos>
+<xref type="see" seq="1554370">涼しい・2</xref>
+<gloss>clear (of sound, objects, etc.)</gloss>
+<gloss>bright</gloss>
+</sense>
+<sense>
+<pos>&adj-na;</pos>
+<xref type="see" seq="1554370">涼しい・4</xref>
+<gloss>composed</gloss>
+<gloss>calm (demeanour)</gloss>
@@ -16,2 +32 @@
-<gloss>cool-looking</gloss>
-<gloss>refreshing to look at</gloss>
+<gloss>unruffled</gloss>
    • A* 2025-02-27 04:54:38 (id#2333418)
    • Comments
      Cool as in temperature or attractiveness?
    • A 2012-06-28 06:05:28 Jim Breen
    • A* 2012-06-25 18:03:58 Marcus
    • Refs
      eij: 涼しげな潮風, 涼しげな音
nikk "ほどよく冷ややかであるさま" (I think there's another sense that 
I can't see)
"涼し気" 158,000 results
    • Diff
      @@ -6,0 +6,3 @@
+</k_ele>
+<k_ele>
+<keb>涼し気</keb>
@@ -12,0 +15,1 @@
+<gloss>cool</gloss>
  6. (show/hide 1 older history records)
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