According to the Taiwan Council of Agriculture, frost was responsible for approximately 30 percent of aquaculture losses in Taiwan during the period 1999-2008. Farmed milkfish, the most important aquaculture crop in Taiwan, is particularly sensitive to temperature variations, and can experience widespread kills whenever temperatures fall below 14°C for sustained periods of time. Temperatures below this critical minimum, however, are not uncommon during the January-March winter months. The purpose of our study is to analyze the possible benefits and the actuarial properties of temperature-based index insurance for the farmed milkfish industry in Kaohsiung County, Taiwan. Weather-based index insurance has been promoted as a cost-effective means of managing risk associated with catastrophic weather events, examples of which include risk transfer products as varied as rainfall insurance in Mali and El Nino-Southern Oscillation insurance in Peru. Of special interest here will be performing accurate assessments of the actuarial properties of a temperature index contract that would indemnify Kaohsiung County farmed milkfish producers based on the value of lower-quadrant daily temperature, which has been shown to be highly correlated with extreme production losses. To assess the actuarial properties of such a contract, we will develop a time series model of daily temperatures lows in Kaohsiung County. Daily temperatures exhibit some special features that must be observed by any reasonable time series model. For example, daily temperatures exhibit strong seasonality with small perturbations. Moreover, seasonal variations exist not only with the mean daily temperatures, but also their variance. Specifically, daily low temperatures are more volatile in winter than in summer. To capture the special features of daily temperatures, we estimate a nonlinear nonstructural time series model of the quantiles of the conditional distribution of daily temperature lows given the observed covariates based on Campbell and Diebold (2005). A simple low-ordered polynomial function is used to capture the deterministic trend and autoregressive lags are used to capture cyclical dynamics of the daily temperature. Also, a Fourier series is applied to model the seasonal components in daily temperature and its variance. However, in contrast to Campbell and Diebold (2005), we model and forecast the lower quantile rather than mean of the daily temperature. We also introduce a phase angle in the low-order Fourier series to allow the peak of daily average temperature to occur at any point in time within a year. The algorithm for computing the nonlinear quantile regression estimates is based on an interior point method described in Koenker and Park (1996). Once the estimates are computed, we invoke bootstrap methods to compute confidence intervals for the contract’s fair premium rate. Our research employs 1974-2008 daily surface temperature data, which is collected and published by Central Bureau, Taiwan, for a weather station located in Kaohsiung County. The farmed milkfish production data in Kaohsiung County also obtained from Council of Agriculture, Executive Yuan, is used to examine the risk-reduction effectiveness of the temperature contracts with different trigger and stop-loss points. The contribution of our paper is not only to provide an alternative method in modeling temperature risk, but also to provide an empirical basis for further, more general discussion regarding the potential benefits of weather index insurance contracts in Taiwan.