Are there any "thermotroph" lifeforms?
No, because temperature is a quantity related to the motion of molecules (or particles) in an ensemble (thus, kinetic energy) but such motion does not have a mechanism to transduce it into some form of useful energy for biological purposes. Chemical gradients are easily stored because of the highly specialized biological membranes (via specific ion channels, etc). Light (photons) can also be used via some proper transducers (photoreceptors), given that there is transduction into chemical energy (i.e. in photosynthesis). But there is no way to 'store' energy from temperature directly in biology because there is no transducer. Temperature differentials in purely physical applications exist, but there is no parallel for biology. All life forms depend heavily on chemical potential and physicochemical gradients, which is deeply rooted in the evolutionary history, you can find an interesting lecture on this topic here.