brew.sh: Move HOMEBREW_TEMP declaration

Additionally, assign HOMEBREW_TEMP based on the host
system (/tmp for Linux, /private/tmp for macOS).

Library/Homebrew/brew.sh

@@ -108,6 +108,8 @@ then
   then
     HOMEBREW_CACHE="$HOME/Library/Caches/Homebrew"
   fi
+
+  HOMEBREW_TEMP="${HOMEBREW_TEMP:-/private/tmp}"
 else
   HOMEBREW_PROCESSOR="$(uname -m)"
   HOMEBREW_PRODUCT="${HOMEBREW_SYSTEM}brew"
@@ -124,6 +126,8 @@ else
       HOMEBREW_CACHE="$HOME/.cache/Homebrew"
     fi
   fi
+
+  HOMEBREW_TEMP="${HOMEBREW_TEMP:-/tmp}"
 fi
 
 if [[ -n "$HOMEBREW_FORCE_BREWED_CURL" &&

bin/brew

@@ -21,7 +21,6 @@ symlink_target_directory() {
 BREW_FILE_DIRECTORY="$(quiet_cd "${0%/*}/" && pwd -P)"
 HOMEBREW_BREW_FILE="${BREW_FILE_DIRECTORY%/}/${0##*/}"
 HOMEBREW_PREFIX="${HOMEBREW_BREW_FILE%/*/*}"
-HOMEBREW_TEMP="${HOMEBREW_TEMP:-/private/tmp}"
 
 # Default to / prefix if unset or the bin/brew file.
 if [[ -z "$HOMEBREW_PREFIX" || "$HOMEBREW_PREFIX" = "$HOMEBREW_BREW_FILE" ]]