They're called macminicolo.net
I've been using them for years, because I thought it'd be a laugh to have a personal server to host my website and email on. I'm still using an old single core Mac Mini, both for my personal use and for hosting websites that I'm building and are in development.
Can't recomend Macminicolo enough.
They're extremely helpful. I think their prices are very good, especially compared to the alternatives. I don't think I've ever experienced an unscheduled outage and even then, I think they've only had a sheduled outage once in the last 5 years and that was only for an hour I think. If you need to have a server that is entirely under your control, but want it in a secure and power-managed server room, I can't think of a better option.
I think they're a great solution. When there's been major OS releases that have required full installs they've offered discounts to their normal charge and roll out the upgrade to all the clients that request it in a single weekend. They also provide the option to have a remote connection to the power supply that your mac mini is connected to, so in the event of a complete crash you can power cycle the device (1st Rule of IT Support - Switch It Off Switch It On).
As I say, been a very happy customer of theirs for years. Highly recommended.