Index: wp-admin/includes/file.php
===================================================================
--- wp-admin/includes/file.php	(revision 7010)
+++ wp-admin/includes/file.php	(working copy)
@@ -182,7 +182,7 @@
 	if( ! $url )
 		return false;
 
-	$tmpfname = tempnam('/tmp', 'wpupdate');
+	$tmpfname = tempnam(ABSPATH . 'wp-content/tmp', 'wpupdate');
 	if( ! $tmpfname )
 		return false;
 
@@ -288,7 +288,7 @@
 }
 
 function get_filesystem_method() {
-	$tempFile = tempnam('/tmp', 'WPU');
+	$tempFile = tempnam(ABSPATH . 'wp-content/tmp', 'WPU');
 
 	if ( getmyuid() == fileowner($tempFile) ) {
 		unlink($tempFile);