Will a lithium ITS battery hold 4 hours at 0 °C and survive 50 °C internal?

Those are the two ends of the same specification and both have to be answered. NZTA states it directly: required battery backup times “shall be met at a temperature of 0 degrees Celsius”, with reduced autonomy acceptable below that. At the hot end, TMR’s 50 °C internal maximum is the design ceiling. LiFePO₄ handles both discharge extremes well, good products retain most capacity at −20 °C on discharge and do not follow the VRLA temperature-life curve at the top end. The constraint is charging below 0 °C, which is why the cabinet heater is a specification item and not an option.