First: There's a specific type of test tube that you should be using for a melting point test; it's called a Thiele melting point test tube. You heat the part that's sticking out, rather than the bottom of the test tube. That gives you better heat distribution/circulation, so that you don't have cold spots in your media (I'm assuming you're using mineral oil of some kind). You can get wonky readings from a plain test tube.
Second: Check the calibration on your thermometer against a few known pure standards. A meat thermometer probably isn't going to be as accurate as you want.
Third: in some instances, raws can absorb atmospheric moisture, which can depress the melting point. You would need to make sure the sample was dry first. I've used a vacuum sealer and silica gel packs to do that before, but it takes a little while.
So, if you don't have hot or cold spots in your tube, your thermometer's calibration is good, your sample is dry, and your sample is 98%+ pure, you should not be getting melting before the minimum temperature in the range. If you get melting out of range, then it's not high purity and there's something else in your sample that's depressing the initial melting point. Is melting complete at the upper end of the range, or is there still something going on there, too?
Worst case scenario, send a few mg off to be tested, and go from there.