Testing a diode's electrical characteristics with temperature control

If you are anticipating an inbound test environment (hundreds to thousands of devices) then I assume you want to test in tape/reel mount with pin probes. I'd suggest:

1. Ambient tests simply at room temperature
2. Room temperature environment High temperature test using self heating (perhaps use a thermal imager to measure temperature if you want close spec)
3. Low temperature testing may be the largest challenge, but perhaps you could use a compressed air cooler. These can get you to -40 degC (with pre-cooled air supply) and I've used them for high power cpu tests with no heatsinks, holding a cpu at about 0 DegC. for example Exair cold gun

If you are testing complete reels, then of course you could use a small environmental chamber, fitting your reel to reel testing station inside.

The use of a peltier is possible, though I think it would slow your testing rate.