heater hose query

[1G1YY]

I am installing an Old Air underdash heater/air con unit. It came with a tap that has a by-pass inbuilt. Since I am using the original de-frost leaver and cable to operate the tap it is inside the cab behind the dash. I am a little worried that when I turn the heater off there may be too much heat radiated off the heater hoses with hot water circulating thru them. One hose runs thru the upper Rh side of the firewall above the kick panel and the other side thru the top of the Lh floor, so about 1.8m of hosing. If I could get some feedback from someone who has a similar setup I would appreciate it.
TIA