Am i responsible for paying the shop again if i just took my car to the shop two days ago and the problem reoccured?

i recently had a leaky radiator replaced on my car which the last mechanic left air in my cooling system to where the coolant wasnt able to circulate through the engine causing it to overheat, so i took it to another certified auto shop and they bled the cooling system of air and got my car up and running to where it wouldnt overheat. thing is….. that was two days ago, and now its trying to overheat again. the mechanic at the shop told me to bring my car back so they can check it out again, but what i need to know is will they be responsible for the problem reoccuring, or will i be responsible for paying AGAIN? do they have to fix the problem free of charge? i just gave them $70 the day before yesterday and i dont have anymore money to put into this car right now. please help me to understand the process for this issue before i take my car back, because i dont know the proper process and i dont wanna get stiffed. THANKS.