The type of thermometer you have works fine, you don't need to purchase another one. They are actually now recommending that you only go to the 10th of a degree instead of 100th of a degree.
"Often, BBT thermometers will boast that they are “accurate to 1/100th of a degree.” For example, the reading will give you 98.63 F instead of only 98.6 F. Except all you need is an accurate reading to the tenth degree, which is available on most thermometers. "
https://infertility.about.com/od/tryingtoconceive101/bb/bbt_thermometer.htm
Step 1: Get a digital thermometer that is accurate to 1/10th of a degree Fahrenheit or 0.05 degrees Celsius. The longer the reading takes, generally the more accurate and precise the thermometer will be. This is because thermometers that take readings in less than 30 seconds generally guess at the what final temperature will be instead of waiting for the thermistor inside the thermometer tip to reach the final temperature on its own. (Our CTO Will will explain this more in a post later on).
https://kindara.com/blog/how-to-get-an-accurate-basal-body-temperature-reading/
I've charted with both, and as long as you chart EVERY DAY your will still see a rise and a tempature change.