This paper investigates abnormal dimension-dependent thermal instability in amorphous indium-gallium-zinc-oxide (a-IGZO) thin-film transistors. Device dimension should theoretically have no effects on threshold voltage, except for in short channel devices. Unlike short channel drain-induced source barrier lowering effect, threshold voltage increases with increasing drain voltage. Furthermore, for devices with either a relatively large channel width or a short channel length, the output drain current decreases instead of saturating with an increase in drain voltage. Moreover, the wider the channel and the shorter the channel length, the larger the threshold voltage and output on-state current degradation that is observed. Because of the surrounding oxide and other thermal insulating material and the low thermal conductivity of the IGZO layer, the self-heating effect will be pronounced in wider/shorter channel length devices and those with a larger operating drain bias. To further clarify the physical mechanism, fast ID-VG and modulated peak/base pulse time ID-VD measurements are utilized to demonstrate the self-heating induced anomalous dimension-dependent threshold voltage variation and on-state current degradation.