Yes indeed all the input work to the compressor will be dissipated as heat to the surroundings.
Since the internal energy of an ideal gas is exclusively a function of temperature, there is no change in internal energy in an isothermal compression.
So, by first law of thermodynamics, an isothermal compression rejects all input work as heat.
Is there such a device? Well yes. All you need to do is have the compression occur so slowly that heat has plenty of time to transfer.
Alternatively what you can do is enhance the conductivity of the walls through which the air moves in the pipes or rotor/stator region.
Seldom does one occur in practice, but it can exist in theory. Most compressors in practice are actually much closer to ADIABATIC COMPRESSORS, which either have insulated walls or operate fast enough that heat transfer is insignificant.
In fact, it is kind of more favorable that a compressor be isothermal than adiabatic. If it is isothermal, you will find that it takes less work input to get the same pressure ratio. The opposite is true for a turbine/expansion stroke, whereby adiabatic is the best design to capture as much work out as possible.
Additionally, it is a common enhancement to a compressor to design what is called intercooling, whereby there is a heat rejection stage between the two compressor stages, and thus it makes the otherwise adiabatic processes, a little closer to the isothermal processes.
So if no energy is actually gained, why do we want an isothermal compression?
Well, because the state of a gas isn't entirely about temperature/energy. It is also about pressure and entropy. For any given temperature, the lower entropy state is the higher pressure. A gas is more ordered at high pressure, as in, we can "do more" with it.
It is also more ordered for a gas to be colder. The hotter the gas, while yes it has more energy, but we cannot really "use" that energy as much as we think we can.