In the absence of details about the insulation, I’ll just make some average kinds of assumptions to get us started.
I’ll assume then we have 12.7 mm copper tubes with 0.9 mm wall, which is pretty common in Australia.
I’m assuming the thin copper wall provides negligible insulation…
I’ll further assume the insulation is a layer of 13 mm of foamed nitrile rubber which is rated at R = 0.3 for a flat surface.
So because the tape is probably significantly thick compared to the pipe I’ll use the fancy radial formula which means the effective R referenced to the circumference of the pipe will be 0.17.
So a 1 metre length of the pipe for instance will suffer losses of
12.7e-3 * 2 * pi /0.17 = 0.469390902 W / K
meanwhile the water within this metre of pipe has a mass of around 0.109 kg. Water at room temperature has a specific heat of 4184 J/K/kg but this water will be a bit warmer and the specific heat will be a little lower, but only a couple of percent or so, let’s just use this number.
.109kg/((0.469390902 W / K) / (4184 J/K/kg)) = 16 minutes.
What this means is that at any given time, the amount of temperature loss that will occur in one minute will be about 4% of the temperature difference between the inside and the outside.
Like if the ambient temperature is 20 deg C and the water is at 70 deg C: then after a minute the water will be at 68 deg C.
It will decrease assymptotically (as the loss rate declines as the temperature gradient declines) but after an hour, the temperature of the water will not be significantly above ambient.