What is the difference between temperature and thermodynamic temperature?
Temperature is more of a relative notion--heat flows from higher temperature to lower temperature, but that's about it. The zero in a temperature scale is meaningless; it is an arbitrary convention. Usually, we measure temperature in Celsius, Fahrenheit, Rankine, etc (note that Kelvin measures temperature as well--but it also measures thermodynamic temperature)

Thermodynamic temperature is such that zero temperature is absolute zero (unlike Celsius, where -273.15&deg;C is absolute zero). It is related to the energy (specifically the kinetic energy) of the molecules of a substance-- for example, in a gas, kinetic energy per molecule is $\frac12k_BT$ (rotational energy, etc can be obtained if you know the type of molecule--but temperature is principally a measure of kinetic energy). It also has strong ties with entropy.

We generally don't use "temperature" in thermodynamics, thermodynamic temperature is more convenient. Temperature is only useful in equations involving temperature difference--whereas equations involving the absolute value of temperature (Arrhenius equation in kinetics, entropy, Maxwell distribution equation, etc) demand thermodynamic temperature.