My car 2007 mercury grand marquis is running hot it used to cool down when pick up speed but now it goes hot and then shuts off????

If it can keep cool when driving fast then the cooling system is working, but only just. The problem could be a restricted radiator that has lost capacity, or a failing water pump, or even a missing fan shroud or air dam, and anything in between. You need the entire cooling system inspected and repairs made. Eventually that engine is going to overheat and be damaged. This isn't something that can be put off either. You can look for simple thing yourself - good radiator cap (no cracks or brittle seal), all hoses are good, make sure lower hose isn't collapsed, or strange bulges on any hose. Check the small hose running to the overflow, that it's got a good seal and isn't cracked. Check the condition of the coolant, if you don't when it was last replaced, then you may be overdue for a flush and refill. If you're doing coolant, that would be a good time to replace hoses and thermostat. Check the cooling fans are running when they should be (when engine is hot, or when AC is switched on). A mechanic can evaluate condition of radiator, water pump, and coolant temp sensor.

I bet your electric fan isn't working. Replace relay? Thermostat for fan? All the things mentioned above should be done. neglect your cooling system, lose your car.