This paper investigates price uncertainties in weather derivatives contracts through a bootstrap approach. Futures prices are computed under a periodic ARMA model in an actuarial framework for two different locations, Paris and Chicago. We show that statistical errors may lead to substantial uncertainties on futures prices with confidence intervals up to 20% of the assessed prices. Looking at the source of uncertainty, this suggests that some efforts have to be done in the modelling of the trend and seasonality in temperature.