I'd guess a post to one of the RISC OS groups might give an answer. ARM processors don't have cooling fans - including early ones with far more speed than needed for a simple task like this. And the early machines which can be easily connected to the web - like the Acorn A5000 - are incredibly well built and reliable, and can be picked up for pennies. Many are still in use for machine control. I've got two later RiscPCs which date back to the mid '90s, and neither has needed any repair. A basic one of these can also be picked up for a few pounds. Simple interfaces which control a few relays often come up on Ebay.
I'd try
There are plenty of enthusiastic and talented 'amateurs' who would write a suitable programme for not much money.
Contact me by e-mail for some suggestions.