Well, 360 degrees is about 100 too hot for almost any brand of polymer clay you're using. Recommended temp is around 265 degrees. You are probably just starting to scorch the clay at that higher temperature. Be careful--the fumes from BURNING polymer clay are not good for your lungs!!
Also, your toaster oven thermostat might be off. Invest in a good quality oven thermometer--a good kitchen store should be able to recommend one for you, and it should cost around $15 for a really accurate one. Put it in your oven right where you'd put your clay, and heat to the recommended temperature for your clay BY THE OVEN THERMOMETER. Then see what temperature that really is on your temperature DIAL and mark it for future use.
Also, toaster ovens tend to heat by cycling between high and low temperatures--heating a little hot, then cooling off, then heating up again. Some ovens are worse than others. And opening the oven door to check will exacerbate this (letting hot air out & making the unit have to heat up again.)
I just realized I've repeated everything penquintrax said!

Some ovens get really hot when they preheat, then level off when they hit the right temperature. It's possible that some spots of your clay are heating more than others & scorching a little--like rolls that burn if you put them in an oven that's in "preheat" mode.
Some famous polymer clay artists used toaster ovens for years with no ill effects, but they made sure they were setting the temperature accurately. Me, as soon as I started doing a lot of baking, I invested in a small convection oven. Fast heat, even heat, no temperature fluctuations or hot spots, preheats steadily and evenly. I love it!
Oh, be careful using wax paper or any paper that can fly up at the corners. The only time I ever saw a toaster oven fire, someone was teaching a little workshop and used a sheet of paper that wasn't completely weighted down, with only a tiny piece in the middle. The corners flew up and hit the top element--and caught on fire. Set off all the smoke alarms in the building (a nursing home...) That was an exciting class! Since then, I use sheets of double-faced corrugated cardboard cut to fit my baking pan. Works like paper, but it's stiff and doesn't flex or fly up.... Plus I think the corrugation acts like an insulated baking sheet, helps the clay bake more evenly.
Hope this helps,
Luann