Which jet engines have the highest thermal efficiency?
Thermal efficiencies are very rarely quoted for aviation gas turbines. The metrics of interest are specific fuel consumption, and power to weight ratio. While a higher thermal efficiency will increase these, SFC and thrust/weight are performance terms that are easier to comprehend, and describe the performance in terms that can directly be used in performance calculations of the aircraft. However, this article from Pratt &amp; Whitney indicates the best aviation gas turbines had just reached about 55% in 2010. But there is no indication of which engine has the highest figure.



Land based gas turbines are more efficient than avaition gas turbines, for a number of reasons. According to this article, the most efficient land based gas turbines, where just under 60%, in 2010. The most efficient installation was a Japanese company, with 59.1% verified on an M701G2 gas turbine at the 1500 MW Tokyo Electric Kawasaki power station in Japan.

Since then GE claimed on the 28th of April 2016, a world record for thermal efficiency, with 62.22%, for a combined cycle plant, in France. GE state that it normally takes about a decade to gain 1% in efficiency. The high thermal efficiency is significantly due to operating at a very high temperature. GE state this plant runs at 2,800 deg. F, but the real number is probably proprietary. They say it's like running the engine at takeoff conditions for its entire flight. As you could imagine, this makes cooling very important. It also takes about 30 minutes to get the turbine from idle to maximum speed. Clearly, that won't work in an aircraft. 



This is the GE 9HA gas turbine. You can see the fuel nozzles (one circled) - and that weight does not matter. So, an aviation turbine will never match this level of performance.

In comparison, the first simple cycle model, developed in 1939 is said to have had a thermal efficiency of just 18%. 

But maximum efficiency is not always the ultimate goal. A product director from Rolls Royce says:


  Everyone would love 60% but the cost is often prohibitive. Not everyone needs a heavy-duty combined-cycle plant. Machines that can achieve baseload within ten minutes such as the Trent 60 are important for the peaking market and a lot cheaper.


Land based combined cycle gas turbines are more efficient than aviation turbines, because;


their design can be optimised with out having to worry about weight. Fuel nozzles in particular are optimised in land based gas turbines.
they can use steam or water inlet fogging (see above!)
they operate at a single rotational speed, so can be optimised for that.