Thermoelectric phenomena resulting from an interplay between particle flows induced by electric fields and temperature inhomogeneities are extremely insightful as a tool providing substantial knowledge about the microscopic structure of a given system. Tuning, e.g., parameters of a nanoscopic system coupled via tunneling mechanisms to two contacts one may achieve various situations where the electric current induced by an external bias voltage competes with the electric current excited by the temperature difference of the two contacts. Even more exciting physics emerges when the system's electronic degrees freedom split to form Majorana fermions which make the thermoelectric dynamics universal. Here we propose revealing this unique universal signatures of Majorana fermions in strongly nonequilibrium quantum dots via noise of the thermoelectric transport beyond linear response. It is demonstrated that whereas mean thermoelectric quantities are only universal at large bias voltages, the noise of the electric current excited by an external bias voltage and the temperature difference of the contacts is universal at any bias voltage. We provide truly universal, i.e. independent of the system's parameters, thermoelectric ratios between nonlinear response coefficients of the noise and mean current at large bias voltages where experiments may easily be performed to uniquely detect these truly universal Majorana thermoelectric signatures.