Hyundai Repair: cooling system problem, head gasket repair, head gasket problem

Question
Overheated engine after hose broke and lost coolant.  I installed new hose and have operated galloper and engine runs normal.  I am loosing coolant with excess pressure from system.  I have changed oil as it was overdue and am looking for signs of head gasket  leakage.  I am adding coolant after each trip due to evaporation and  overflow.  Can a faulty rad cap or missing thermostat cause overheating where it reaches above normal temps.  I am trying to eliminate all possibilities before getting into a head gasket repair.  As i said engine is running  good the same as before and no visible indications of head gasket problem other than the pressure.

thanks for your help

Answer
While I'm not familiar with the Galloper, this is a general cooling system question, so I'll provide what information I can.

A missing thermostat cannot cause overheating.  A faulty radiator cap can cause overheating by not pressurizing the system, but this would be very unlikely.

What needs to be done is a good cooling system audit.  Start by operating the air conditioning.  If this vehicle is set up like the other Hyundais I've seen, the radiator fans should operate.  If not, check the fan fuses and other electrical components in the fan system as necessary.  If the fans operate normally, proceed to check as follows:
-- remove radiator cap (only when cool) and inspect radiator tubes.  If clogged, you'll need a new radiator.
-- start engine and observe coolant in radiator.
-- coolant should not flow until operating temperature is reached.  This will not apply if the thermostat is removed.
-- coolant should begin to flow when the thermostat opening temperature is reached.  If you cannot see the coolant flow through the radiator filler neck, monitor the temperatures of the radiator hoses by grasping them (carefully).  Before coolant flow, the upper hose should be significantly hotter than the lower.  After coolant flow, they should be about the same temperature.
-- a short while after the coolant begins to flow, the radiator fan(s) should begin to run.
-- the radiator fan(s) should continue cycling on and off as necessary.
-- the coolant should not boil prior to the fan(s) cycling on.