How can I test a hex Schmitt trigger?
Apply a logic level to each of the inputs, and see what the outputs give. If they're inverters the output should be 0 V when you apply 5 V (or whatever your supply voltage is) to then input. Connect the input to ground and you should get 5 V out.  

It's unlikely that you fry it through the heat of soldering. ICs withstand temperatures of 300 °C on all pins simultaneously for several seconds. ESD may be another issue.