A heated bed is going to be optional when printing with TPU. It’s not a requirement, but many will recommend it to get the best results. This will depend on the exact type of TPU that you are using, as some work exceptionally well at room temperature.
TPU is naturally very good at adhesion to a bed when compared to other types of filaments. Some like the YOYI TPU 3D Printer Filament do require a bed temperature of 60°C - 80°C (140°F - 176°F), which is higher than most other TPU’s.
If you don’t want to use a heated bed, it’s important to double-check the temperature, but for most TPU’s, it won’t be an issue.