Cosmological parameters from WMAP 5-year temperature maps

I calculate a hybrid cross-power spectrum estimator from the WMAP 5-year CMB temperature maps, discuss the goodness of fit, and then constrain cosmological parameters. The spectrum and results are generally consistent with previous results, though the power spectrum error bars are slightly smaller and there are small shifts at high l. The small improvement in error bars is obtained at very low numerical cost but does not significantly improve parameter constraints. I discuss the accuracy of the likelihood model and how constraints on the optical depth translate into constraints on the reionization history allowing for helium reionization. In the appendices I propose a simple reionization parametrization that determines the history in terms of a midpoint reionization redshift, and suggest a new likelihood approximation for chi-squared-like distributions with varying skewness.