Aquilo Heat Piping to second Lithium Brine island

I searched for this but came up empty... for those of you who have run out of Lithium in your initial patch, do you run piping from your main heat towers, or do you build a new heat source out on the new lithium island? That's my question.

In my case, the distance to the next closest lithium source is more than 650 heatpipes. I'm hoping to avoid setting up logistics all the way out there to support keeping a heat tower functional, but that seems like such a long ways away. Not to mention, I'll have to heat that 650 tile stretch anyway, for the fluid piping.

Love to hear from anyone who has already done this.