In current aeronautical research, rapidly‐responding thermocouples and hot‐wire anemometers are required. The use of oxide cylinders coated with more or less thin layers of metal effects substantial improvements in rates of instrument response. The theory and results of numerical calculations for six typical situations are given. It is shown that for ratios of metal thickness to over‐all radius of 0.1, response amplitude gains of the order of 4 or 5 are to be expected as compared with typical gains of the order of 10 or more for infinitesimal shells (surface layers).