No. The top hose goes to the engine. The bottom hose feeds from the engine to the heater core back to the radiator.
Top hose of the heater core goes to the thermostat housing. The lower hose goes the the fitting behind the A/C compressor.
one large hose from bottom of radiator to side of water pump. other large hose from thermostat housing to top of radiator. one heater hose from water pump to heater core, I think this one has a Y in it if there is a rear heater other heater hose from heater core to somewhere on top the engine. If there is a rear heater, its return hose goes to a fitting on the radiator.
There are two heater hoses. One goes from the head, or top of the engine, to the heater core in the passenger compartment, the other goes from the heater core to the water pump, thermostat, or some other part of the water jacket. Check the instructions for the flushing kit.
heater core
"Does the top or bottom heater hose from the firewall go to the water pump on a 1991 Dodge Dakota V6?" The top heater hose from the firewall goes to the water pump and the bottom hose from the firewall goes to the top of the block where the temperature thermostat housing is located.
the heater hoses usually lead away from the thermostat and go into the fire wall. On the other side of the firewall is the heater core. the top hose on the radiator goes into the thermostat most of the time
On a 1989 Chevy Celebrity the heater hose leaves the water pump via a hose barb then runs along the top of the passenger side frame rail and then into the heater core. The heater core is in the firewall below the blower fan on the passenger side of the car. The return hose leaves the heater core and runs along the firewall then to the water outlet below the thermostat.
Generally the coolant goes in the bottom of the heater core and out the top only because the coolant makes less noise this way if there happens to be trapped air in the system, otherwise it doesn't matter.
Thermostat opening too soon? Heater air bound and needs to be bled
Thermostat housing It is probably the quick connect fitting. The hose goes from there to the heater core. I had to replace mine last year.
Thermostat housing