The file extension HDT is used for so-called High Dynamic Tone or 32 Bit Toning Options files of the image editing software Photoshop. These files contain tone curve values that can be used when converting 32-bit High Dynamic Range (HDR) images to 16-bit or 8-bit color depth.
An opened 32 bit HDR image can be converted to another image mode with 'Image -> Mode'. If you select an 8 or 16 bit mode, you can load and save HDT files in the following window 'HDR conversion'. You can also use the small arrow to display the corresponding tone curve and the histogram of the image.