engine cooling system....broken???

[83-z]

i just got my 83 z28 runing and now it seems to be overheating... hasent left house cause im still fine tunning shit and had to work on trans.....but the upper and lower hose are warm to cold and not pressurized..( not stiff at all ) and the coolant in the radiator must stay there but the lines from the block to my heater core get hot and pressurized....i dont know if it could be a stuck thermostat or what but im kinda stumped on this one.... thanks for your help!

[MonteC]

how hot does it get?
mechanical fan or electric fan?
does the coolant level drop in the radiator, in other words do u have to keep filling the radiator up every week or so?

if the coolant isnt leaking out anywhere and the level stays constant then im gonna say replace your thermostat.