Space-time noncommutative theories at finite temperature

We analyze renormalization and the high-temperature expansion of the one-loop effective action of the space-time noncommutative ${\varphi }^4$ theory by using the zeta-function regularization in the imaginary-time formalism (i.e., on $S^1\times {\mathbb{R}}^3$). Interestingly enough, there are no mixed (nonplanar) contributions to the counterterms as well as to the power-law high-temperature asymptotics. We also study the Wick rotation and formulate assumptions under which the real and imaginary-time formalisms are equivalent.