diff --git a/.github/workflows/cross-compile.sh b/.github/workflows/cross-compile.sh
index ff5b67fc4..cd526223f 100755
--- a/.github/workflows/cross-compile.sh
+++ b/.github/workflows/cross-compile.sh
@@ -12,7 +12,22 @@ if [[ "$goos" == "android" ]]; then exit; fi
 # Cgo would then need a C cross compilation setup. Not worth the hassle.
 if [[ "$goos" == "ios" ]]; then exit; fi
 
-echo "$dist"
+# Write all log output to a temporary file instead of to stdout.
+# That allows running this script in parallel, while preserving the correct order of the output.
+log_file=$(mktemp)
+
+error_handler() {
+  cat "$log_file" >&2
+  rm "$log_file"
+  exit 1
+}
+
+trap 'error_handler' ERR
+
+echo "$dist" >> "$log_file"
 out="main-$goos-$goarch"
-GOOS=$goos GOARCH=$goarch go build -o $out example/main.go
+GOOS=$goos GOARCH=$goarch go build -o $out example/main.go >> "$log_file" 2>&1
 rm $out
+
+cat "$log_file"
+rm "$log_file"