Measurement and analysis of the temperature dependence of avalanche gain and excess noise in InAs electron avalanche photodiodes (eAPDs) at 77 to 250 K are reported. The avalanche gain, initiated by pure electron injection, was found to reduce with decreasing temperature. However no significant change in the excess noise was measured as the temperature was varied. For avalanche gain > 3, the InAs APDs with 3.5 µm i-region show consistently low excess noise factors between 1.45 and 1.6 at temperatures of 77 to 250 K, confirming that the eAPD characteristics are exhibited in the measured range of electric field. As the dark current drops much more rapidly than the avalanche gain and the excess noise remains very low, our results confirmed that improved signal to noise ratio can be obtained in InAs eAPDs by reducing the operating temperature. The lack of hole impact ionization, as confirmed by the very low excess noise and the exponentially rising avalanche gain, suggests that hole impact ionization enhancement due to band "resonance" does not occur in InAs APDs at the reported temperatures.