As the engine inlet temperature increases, Is more heat energy provided by air? if yes then can we utilize that heat energy to produce more thrust?
I guess the heat you ask about is the temperature increase that goes with the precompression of air ahead of and in the intake. This heat is further increased in the compressor, according to the ideal gas law. If there were no temperature increase during compression, the engine could burn a lot more fuel and produce a lot more thrust.
To use the precompression heat would mean that first the air flows through a heat exchanger in order to transfer that heat to something that can produce thrust from it. That something would have to heat the air in the combustion chamber or after the last turbine stage in order to increase thrust. At both stations the gas temperature is a lot higher than the heat that can be harvested from the intake air. Now you first have to run that heat through a heat pump to make it useable (or, if you turn this around, you need a heat pump to produce a medium cold enough to harvest heat from the intake air in the first place!).
I hope you start to see how much more complicated and heavy this kind of engine will become. There have been attempts to recuperate the heat of the exhaust flow in turboprops, but so far nothing of that kind has ever entered production.
Heat is an unfortunate and unavoidable by-product of energy conversion. Some of it can be transformed into propulsive energy: the steam engine, steam turbine and Sterling engine do this. Another way that heat energy can be transformed into propulsive energy is by injecting water in the hot stream: if that stream is hot enough the water droplets transform into vapour within the engine, and that provides thrust.
Having said that, gas turbines have pretty high efficiency at full power output, in the order of 40%. That means that 60% is waisted as heat - in some power stations the waste heat is used to power a steam turbine, raising the total efficiency to over 60%. A bit of a heavy set-up for an aircraft though..