At low temperature, the kinetic product is typically favored. However, if the thermodynamic pathway also has a pretty low activation energy, then you don't want or need a very high temperature. For kinetic control, you want a temperature that is high enough that the reaction will proceed under a reasonable amount of time. For thermodynamic control, you want a temperature that is high enough that the reaction is reversible and approaches equilibrium in a reasonable amount of time. The second temperature is higher than the first temperature if the second reaction also has a higher activation energy.
To answer your question, though, the thermodynamic product wouldn't ever form "faster" than the kinetic product (assuming that we are talking about two competing reactions). The thermodynamic product would predominate at equilibrium only because it is more stable.