Okay, say we have a tidally locked planet that has one side facing its star. On the side that always faces the star, my question is will that side facing the star always be increasing in temperature? If the side is always facing the star, it doesn't have time to cool.
Hot objects radiate heat. The hotter something is, the faster it radiates heat.
The side of the planet that faces the sun would heat up until the rate at which it is absorbing heat from the star is equal to the rate at which it is radiating heat. Once it reaches this point it will be stable, and neither heat up more or cool down.
As a simple analogy, consider standing next to a heater or a fire. You will heat up, but you won't heat up forever. You will reach thermal equilibrium.
You're asking if the temperature of the side facing the star will increase without bound. Almost anytime you're talking about a real, physical system, "without bound" just doesn't happen. Think about it - if the temperature was always increasing, eventually the planet will be hotter than the star its orbiting. At that point, why would it continue to get hotter? At some point, the system will settle into an equilibrium where the incoming radiation is balanced by the rate of cooling, at which point the planet won't get any hotter.