A fine mesh will work well, provided the mesh size is quite small, otherwise you can get some odd moire effects. Nice thing about mesh is that its usually fairly flat across all wavelengths.
For calibrating, you can just apply a suitable emissivity adjustment (same can be done for all windows/filters). For example if the mesh/window etc has a 50% opacity, just apply this to the surface emissivity of the taget. Eg, target emissivity of 0.8 with a window of 50%, set emissivity to 0.4.
If you can't work out the opacity of your filter, then try to do a calibration at the highest temperature you can get to with your camera, ie read the temperature of a target, place the filter in front, then adjust the emissivity until it reads correctly again.
This may not work with all cameras though, depending on how the brightness is calculated. Some cameras use a table (precalculated brightness taking into account all optical/electrical factors in the instrument) which may be limited to the working range of the camera. Other instrument that use a mathematical model may by highly innacurate outside the working range.
Depending on how hot you want to measure, you could try calibrating a standard silicon based camera (eg phone camera). You ideally need to lock down as many parameters as possible (aperture, shutter speed, gain, etc) then use a NIR bandpass filter infront of the camera, though you can do it without a filter provided theres no ambient change in the scene. To calibrate it you might need to find a couple of hot sources of known temperatures though. Dynamic range on most 'phone' style cameras though is only 8-bit so you really dont get much dynamic range, especially given the energy from the high temperatures. Some 'machine vision' cameras work at 12 or 14 bit.
Another fun thing you can do with an optical camera is use the Bayer filter to provide ratiometric measurements, though for this you need access down to the subpixel level. Once again though, the limited dynamic range is a real problem.