The jet engine efficiency is unfortunately more complicated than just a one-to-one function between static Turbine Inlet Temperature and efficiency. Thermodynamic efficiency of a turbine engine is defined as the useful generated power extracted from the chemical energy added by the fuel.
The following is extracted from a paper format uni book on aircraft gas turbines.

Station 0 is for the engine inlet, the other station numbers are:
- Compressor inlet.
- Combustion chamber inlet.
- Turbine inlet.
- Turbine outlet.
- Engine exhaust.
Energy IN
The heat flow $\dot{Q}$ added to the engine is:
$$ \dot{Q} = \dot{m} \cdot c_{pg} \cdot (T_{3t} - T_{2t}) \tag{1}$$
With $\dot{m}$ = mass flow through engine, $c_{pg}$ = gas constant, $T_{3t}$ = total temperature at turbine inlet. Total temperature is the temperature reached when a gas flow is compressed isentropically, measured in the stagnation point, and defined as $$T_t = T + v^2/(2 * C_p) \tag{2}$$
So energy IN is a function of:
- Static Turbine Inlet Temperature
- total mass flow
- gas flow velocity at the turbine inlet.
Useful power OUT
The power delivered by the gas generator is:
$$P_{gg} = \dot{}m \cdot c_{pg} \cdot T_{4t} \left[ 1 - {\left(\frac{p_0}{p_{4t}} \right)}^{\frac{\kappa_g - 1}{\kappa_g}} \right] \tag{3}$$
with
- $T_{4t}$ = stagnation temperature at the turbine outlet.
- $p_0$ = static pressure at engine inlet, a function of air density and airspeed.
- $p_{4t}$ = stagnation pressure at the turbine outlet, which depends on how much energy the turbine has extracted from the gas flow.
Efficiency
If we could vary the $T_{3t}$ only and keep the other variables constant, we could indeed get to the sort of function sought after - but we cannot. Increasing T.I.T creates more thrust, accelerates the aircraft, increases inlet pressure, increases turbine outlet pressure etc.
From Gas Turbine Theory by Saravanamuttoo/Rogers/Cohen, page 81:
The large number of variables involved make it impracticable to derive algebraic expressions for the specific output and efficiency of real cycles.