This paper develops a search-and-matching model that incorporates temporary unemployment and applies the model to study the labor market dynamics of the COVID-19 recession in the US. We calibrate the model using panel data from the Current Population Survey for 2001-2019, and we find that the model-based job finding rates match observed job finding rates during the entire sample period and out-of-sample up through July 2020. We also find that the Beveridge curve is well-behaved and displays little change in market tightness in 2020 once we use the calibrated model to adjust for changes in the composition of the unemployed. We then use the model to project the path of unemployment over the next 18 months. Under a range of assumptions about job losses and labor demand, our model predicts a more rapid recovery compared to a model that does not distinguish between temporary and permanent unemployment and compared to professional and academic forecasts. We find that in order to rationalize the professional forecasts of the unemployment rate, some combination of the vacancy rate, job separation rate, and recall rate of workers on temporary layoff must deteriorate substantially from current levels in the next several months.