The demand for higher power density in electric traction applications has led to compact design requirements for traction drives complicating its thermal management. Therefore, the traction drive's thermal management has to be addressed by its design and/or control. Normally, the traction inverter becomes the bottleneck in providing the transient rated peak torque at zero and near zero speeds due to peak current conduction for longer fundamental frequency cycles. This paper presents thermal management strategies based on both current limitation and on an alternate modulation scheme that redistributes the losses between the IGBTs and diodes of the highest current carrying leg at very low modulation indices. The presented strategies avoid or delay the over-temperature junction failure due to high conduction losses. The proposed strategies enable the drive to provide the rated peak torque at zero or near zero speeds while avoiding or delaying thermal failure.