Does A Big CI Stroked SB get to a point where It is hard to keep cool?

This may sound like a dumb question. I have seen stroker small blocks up to 440 CI. Are they hard to keep cool on the street? Here is my thinking. A 440 big block has more internal coolant capacity (bigger block, more space inside for coolant passage), so a 500 HP 440 would have more coolant flowing through it. But, if you stroked a SB to 440, would that small block have the capacity to allow enough coolant to flow through it to actually cool it? I assume it is partly a function of radiator size/capacity, but you can only put so big of a radiator on a 69 A body.
No