I have the same error with our Jenkins after an upgrade to 1.539. It extract the war file into our /tmp folder but this one is cleaned by some other process and I can't guarantee that all files will not be deleted... This is a horrible behavior for us and so, it's blocker.
Nov 20, 2013 3:29:14 PM org.eclipse.jetty.util.log.JavaUtilLog info
INFO: jetty-8.y.z-SNAPSHOT
Nov 20, 2013 3:29:14 PM org.eclipse.jetty.util.log.JavaUtilLog info
INFO: Extract jar:file:/usr/lib/jenkins/jenkins.war!/ to /tmp/jetty-0.0.0.0-8181-jenkins.war-_jenkins-any-/webapp
Nov 20, 2013 3:29:16 PM org.eclipse.jetty.util.log.JavaUtilLog info
INFO: NO JSP Support for /jenkins, did not find org.apache.jasper.servlet.JspServlet
Jenkins home directory: /data/jenkins found at: System.getProperty("JENKINS_HOME")
@dev, I have try to use your solution and I define another tmp folder for Jenkins but it still extract its war file into our /tmp folder.
Here an echo of my command line exectuded when I start the service.
Starting Jenkins
JAVA_CMD : /usr/java/java6/bin/java -Djava.awt.headless=true -XX:MaxPermSize=512M -Xms512m -Xmx4096m -DJENKINS_HOME=/data/jenkins -jar /usr/lib/jenkins/jenkins.war
PARAMS : --logfile=/data/logs/jenkins/jenkins.log --webroot=/data/jenkins/war --daemon --httpPort=8181 --ajp13Port=8010 --debug=5 --handlerCountMax=100 --handlerCountMaxIdle=20 -Djava.io.tmpdir=/data/jenkins/tmp --prefix=/jenkins --accessLoggerClassName=winstone.accesslog.SimpleAccessLogger --simpleAccessLogger.format=combined --simpleAccessLogger.file=/var/log/jenkins/access_log
Thx for any help 
Winstone has ceased the development upstream, so we are the one maintaining it. That obviously doesn't make sense.
Another benefit is that this would also allow us to start delivering features that depend on WebSockets, etc.
This work involves writing a new driver code that accepts options that Winstone accepts but instead drive Jetty. For this purpose, I have refactored Winstone to explicitly list up all the options in use.
The general option compatibility is important so as not to disrupt existing deployments, even if we might consciously decide to skip some uncommon options if those are deemed too hard to match.