Does anybody know how,
even if it is possible, to install CoreOS on terminal.com ?
The first question for Terminal.com would probably have to be what underlying technology they use to run their VMs (if they even are full virtualization). They claim their VMs only take 5 seconds to startup. This to me almost sounds like they might be running some sort of container technology (Docker or regular LXC) which wouldn’t work to run CoreOS.
However, if it is actually a virtual machine, you might be able to adapt https://github.com/ibuildthecloud/coreos-on-do to use their Ubuntu 14.04 image to kexec a CoreOS install.
I’d be fairly wary of using this for production loads though since it would be pretty unreliable and unsupported. If it is cost that you are after, you might check out Digital Ocean or another provider that better supports CoreOS.