Abstract: A nonlocal viscoelastic Euler-Bernoulli beam model is developed to investigate the thermoelastic parametric resonance stability of a pulsating-fluid-conveying carbon nanotube (CNT) in different temperature fields. After discretized by the Galerkin method, the governing equation with small scale and thermal effect terms is solved by the averaging method and the analytical expression of stability boundary is obtained. It is found through numerical examples that the stability of the CNT in higher temperature fields is much poorer than that in lower ones. Increase of temperature change and nonlocal parameter in lower temperature fields can enhance the stability of the CNT, but it will reduce in higher temperature fields. Increase of viscoelastic coefficient in higher and lower temperature fields can both enhance the stability of the CNT, but this viscoelastic effect of the material on the stability will decrease in higher temperature fields. The conclusions drawn in the present paper are expected to be helpful for the structural design and thermoelastic vibration analysis of fluid-conveying nanodevices.