Got it running with Heroku.
To do it:
start with Getting started with Java, clone an example project until the create command
continue with the link below
try the
heroku-deploy CLI plugin.
It has a mechanism for
deploying executable JAR files. You can run a command like:
$ heroku deploy:jar --jar powerMonitor.jar
You will also need to put a Procfile in the same directory you run the command. The Procfile must contain the process name and the Java command. It might look like this:
job: java -jar powerMonitor.jar
The Procfile is in the cloned project, just edit it like in the instructions.
PowerMonitor.jar is my application, make sure to write with the same letter case.
No need to install Java like the other vps services (which I couldn't get to even start working with).
The regular support led me in some wrong ways until I got a "java man" to give the above answer which work.