Air pressure in the engine

Well one hot and one cool hose means the coolant is not flowing thru the radiator. That could be from a defective pump, closed thermostat, air in the system, or a blockage in the radiator. You might try running the engine with the thermostat out to check flow.

I doubt its anything electric.
Are you sure the radiator is full of coolant ?
Do both radiator hoses get hot when the thermostat opens at 195 degrees ?
Do both heater hoses get hot after running the engine for 5 min ?

you could have an air lock would bleed heater hoses

!st check and make sure the water is flowing in the radiator, then check
the timeing, Mazda will run hot if the timeing is rong.

indicates an air lock in the cooling system
could be from a failing head gasket ( do a compression test)
have a coolant pressure test done to find the leak
possible a water pump seal leaking when running
check sump oil for greying color ( failure of the housing behind the pump impeller

it sounds like one of several problems radiator needs flushed , water pump is bad or going, thermostat is bad, pin hole in one of the hoses, cracked head, hole in radiator, hole in heater core.if core is leaking you will notice water on the floor inside the car on pasenger side. if radiator has hole when you fill radiator with coolant it will leak froom fins sometimes only when hot. thermostat bad your car will read hot and or cold always. if stuck open cold, if stuck closed hot, after about 15 20 mins of running engine will cause radiator to boil over to over flow tank.never open radiator cap when engine is hot :) burn hazard.if pump is bad or going will notice gauge reads hot intermittent or always. will boil in to overflow tank. if head is cracked will notice water comming from side of engine block or in oil when you change oil. if radiator needs to be flushed will notice scale or gunk on radiator cap
(if you think you need help or do not have tools to perform please take to a machanic)

YOU SHOULD FLUSH ENGINE BLOCK BEFORE INSTALLING NEW THERMOSTAT.YOU NEED RADIATOR FLUSHED AND ENGINE BLOCK FLUSHED.ALSO REPLACE THE RADIATOR PRESSURE CAP.

use your hand on both hoses into and out of the heater core to see that they are hot. if not the core is plugged and needs to be replaced. before you do that squeeze the hose upper and lower and the heater core hoses to make sure there is no air trapped in the system. be very very careful of the fan while you are doing this.

Try this:  
First, turn the hearer temp control to full 'Hot' setting.  Then, when the engine is COLD, open the radiator cap.
If you see the coolant, close the cap and add more coolant to the overflow tank, but only up to the 'Full' mark.
If you don't see any coolant when you open the cap, pour in some coolant and let it settle down.  Keep doing this until it stays full.  Also fill the overflow tank to the 'Full' mark.
Good luck.

Have you tried replacing the water pump? Sounds like the water pump is not circulating to water.
Hope this helps!
CastleTowery