Overheating no heat civic?

So I bought this 04 civic and it would over heat and would stop blowing heat I replaced thermostat with one from autozone I found the thermostat it had was cut so go figure so after replacing it would still overheat I took it to a shop they said that thermostat was no good so they replaced it car was fine for 3 days and again it started over heating and no heat I noticed lower coolant hose was cold before replacing thermostat myself then those 3 days after shops thermostat hose would be hot. Now that it overheats/no heat it's cold again. Could it be thermostat Should I buy an oem Honda thermostat thanks

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