B777 Captain reported refusing the aircraft due to extreme weather and low temperatures; lack of effective ground heaters and preconditioned air and a deferred APU made it impossible to warm the aircraft to operating temperatures.

Narrative

Aircraft X was dispatched to fly a ZZZ-ZZZ1. Among the deferrals was an inoperative APU. We proceeded to Gate XX; and a Company B747 was still occupying our gate because of a frozen belt loader and aft jet bridge stuck to the airplane. The situation delayed the tow of our aircraft from the International Terminal. When our aircraft arrived; caterers opened doors 2R and 4R; further cold soaking the fuselage. Cargo doors were opened compounding the cold soak. The temperatures were so bitter; the First Officers and myself could not get on the plane. Once the doors were closed; the fuselage temperature was down to 19 Degrees F in the coldest zone. The situation was not improving since external air was not connected to the aircraft because of Stage 2 winds. The Flight Attendants would not enter the aircraft because of the temperatures. I supported that decision. Our crew water bottles began to freeze in the cockpit. We all intermittently had to return to the jet bridge to warm up. My feet were numb. Ramp acquiesced and hooked us up to one hose of heat. That had no effect on the cabin. A second hose was then hooked up; and after two hours; that brought the cabin into only the 30degs. Maintenance then came to me and said the lavatories were not serviceable because the dump valves were frozen. The lavatories themselves began to freeze. At that point maintenance took the airplane out of service. Operations immediately took control of that decision and reinstated the jet back into service. Operations then called me and asked if I would sit at the gate with both engines running. I said I would not in the interest of safety sit with both engines running for hours at the gate. Ramp found an external air cart we would need for the start. They cautioned me that they had attempted 4 air cart starts earlier in the day and all failed. I called the Operations Manager to express my concerns. He suggested we attach the air cart to the packs and run them. I kindly ended the call and hung up. We have no procedure in our manuals for this. In addition I have been on the B777 for XX years and have never heard of this. To reinforce the implausibility of this idea; one of the Mechanics working our flight said that was not possible. Finally; [they] wanted me to taxi around for a couple of hours in hopes the lavatory lines would thaw. We all sat in the cockpit intermittently trying to preflight between trips to the jet bridge to warm up. I felt really uncomfortable being tasked to release the parking brake with no permission or paperwork to do so. In addition; Maintenance has the ability to do this themselves. The ideas became more cockamamie and desperate. It was apparent I was the only one to just stop the crazy ideas being floated. I called the Operations Manager and was connected to Captain. It was at this time I stated I was refusing the airplane; and together he patched me through to Dispatch. It was not until sometime later they cancelled the flight. I made multiple PA announcements at the gate to the passengers during the entire process. The last announcement was misconstrued by the gate agents as me cancelling the flight. I made no such announcement. The Flight Attendants left the boarding area; I never saw them the rest of the night. My oversight was not making an ELB entry 'Unable to Operate.' I tried my best to find another B777 we could use; that attempt was futile. Maintenance said it would take hours to thaw the airplane in the hangar. The Maintenance Supervisor wanted to put two independent heaters in the cargo compartments. That idea was implausible because each unit weighed 600 lbs. and would have to be carried by hand from a flat bed lift. By the end of the night; we left the airport at XA AM trying our best to do our job with an airplane that should never have been routed through the weather conditions in ZZZ that night. I had tangible concerns for the safety of my crew and passengers.