Tomcat is a little heavy and intrusive for simple content serving. Switch to embedded Jetty instead, which shouldn't require any temporary directories at all.
Configure a static file server and Jetty logging should be automatically routed to SLF4J if present.
We may stick with Tomcat for guise host for a robust hosting experience. But that will require planning and more work, including allowing configuration of e.g. reverse proxies to allow Apache to be placed in front.