High-temperature threshold characteristics of a symmetrically graded delta-doped InAlAs/InxGa1-xAs/GaAs (x=0.5 -> 0.65 -> 0.5) metamorphic high electron mobility transistor (MHEMT) have been investigated. The thermal threshold coefficients, defined as partial derivative V-th/partial derivative T, are superiorly low at 0.9 mV/K from 300 to 420 K and at -0.75 mV/K from 420 to 500 K. An interesting polarity change of the thermal threshold coefficient was observed around 420 K due to the variation of thermal modulation effects. The present MHEMT device, with stabilized thermal threshold variations and superior high-temperature linearity characteristics, is promising for high-temperature circuit applications.