A 2000 town car limo was build just in tolerance for the 4.6 engine capability. Even at brand new it would overheat if you push it to hard. It is older and less efficient and it over heat in general if you push it. The question would apply to other engines: Can I move the heater cores meant for warming the vehicle to the front of the car to adding extra cooling power for the engine?
Adding radiators might help – if the problem is insufficient radiator capacity – but I suspect that you would do better to find the root cause of the problem. For example, in an older car it could be:
- A failed thermostat, or
- A water pump that's impeller is eroding away and is no longer pushing enough volume of water, or
- A hose on the suction side of the water pump that is collapsing and restricting flow.
In general I would expect that the design of the cooling system would handle running the car on a very hot day with maximum load up a long hill (or perhaps the way an engineer would think about it – the capacity should be adequate to cool the engine at full power on the hottest "normal" day). So rather than reengineering, I would go looking for the cause and correct that. It is more likely to keep the car running well and it will certainly be less expensive and time consuming.
One problem with adding extra radiators is that they will need a supply of cool air to work well, so installing them in the front (with other radiators behind them) will probably result in a loss of efficiency of the other radiators.
You could use the heater core as a way to provide extra cooling, in fact when a car overheats you could turn on the heat and the blower to full speed in order to prevent overheating.
However, there are other ways to solve this problem, you could check the coolant level, and the condition of it. If not sure replace it. Also check the thermostat and replace if you are replacing the coolant. Check the radiator fan if it working. Also check if the radiator is clean, and nothing blocks the air flow, do check very thoroughly that one because it might have hidden areas.
If all the above doesn't meet your demands, you could start thinking in upgrading the radiator and the radiator fan.
Instead of doing that, I would suggest replacing the existing radiator at the front with a new one - as you suggest in the question, a 16 year old radiator will be much less efficient than a new one, and will have lost many of it's cooling fins, and be full of sludge. You may also be able to get a custom radiator made with more cores than the standard one, if there is room to fit it (a new modern radiator may well be thinner than an old one, so you might be able to fit three cores in place of two, for example)
At the same time, give the rest of the cooling system a thorough flush through (in the opposite direction to normal) to get rid of any sediment that may be restricting flow, and replace the thermostat.
Also, give the rest of the engine and running gear a good service - anything that helps to reduce the load will also reduce the amount of heat generated...