Understanding local heating effects in nanoscale constrictions has both fundamental scientific importance and possible technological implications. However, monitoring temperature in such small length scales is very challenging. To address this problem, we use a specific noise measurement scheme to probe local heating due to applied bias voltage in a low temperature break junction setup.  We focus on atomic gold junctions with a single fully-open transmission channel, to effectively suppress shot noise contributions despite the finite bias voltage. At the same time, we probe a considerable contribution from the thermal noise. In spite of the extremely high current densities in our experiment, we do not find indication for local heating up to bias voltage of 300mV. Moreover, the junction behavior is consistent with Landauer formalism even at high bias voltage. These results are found to be in variance with previous results at room temperature in which local heating was reported.