How can I uniformly blur the entire image from a thermal camera optically?

Yes. The practical approach is to add a diffuser in front of the thermal lens, but the material must still transmit the wavelengths your thermal camera uses. Community suggestions included thin plastic materials such as a document sleeve/protector or a transparent plastic bag, which may pass enough thermal radiation to create a soft, low-detail image. A proper diffusion filter could also work if your camera can mount one and the material is transmissive for your camera’s spectral band.

For a more uniform and repeatable result, a transmissive filter could be deliberately roughened/frosted so it acts as a diffuser. The key limitation is spectral compatibility: many materials that look clear in visible light are not transparent in thermal IR, so testing is essential.

In short: yes, an optical blur is possible, usually by placing a partially IR-transmissive diffusing material in front of the lens. Start by testing simple plastics, then move to a purpose-made or roughened transmissive filter if you need a cleaner, more consistent effect.