You could even use one length of garden hose with a beer line running through it and just cut a slit in the hose out by the tap and silicone it shut, using the rest of the hose as a return line for the coolant.
That would be what I had originally envisioned....
Oh and it doesn't have to be an open bucket in the cool room. That's just asking to get kicked over when swapping out the first or tenth keg!!!
If you plumbed the hose into some sort of metal box (like a small radiator) and bled it off as such, your cool room would keep that cool. Just gauge the size such that when you turn on the pump, and the reservoir and the line contents mix, you get minimal gain of heat across the complete system.
If you were to use say a garden hose of 1.5cm internal diameter, and a beer line with 1.1cm external diameter, you’d require approx 0.3L coolant per metre. Over 5 metres you’d need 1.5 Litres (this would be outside your cool room)
If you keep your cold room at 5C (40F) and your external temp wouldn’t exceed 35C (95F), to realise a temp increase of 1C over the system you’d need a reservoir of about 5Litres water per metre of line.
Of course realistically there won’t be such a swing in temp as most of the line will be insulated and indoors. If there were a swing of say 70F room temp to 40F cool room the reservoir only needs be about 1.3L per metre of beer line…
(That would be the initial swing without the need for turning on the pump in advance of a party)
Sorry for the long post!