In general terms I would say yes, it's definitely possible for a moderately handy person, armed with some safety rules, a multimeter, a good set of insulated hand tools (what a great excuse to get them if you don't have them!), a service manual, a parts diagram and Internet, to repair pretty much anything in a dryer. Beyond that, some people are just not comfortable working with electrical devices (when they are de-energized of course) and some people are not comfortable working with combustible gases. If you're OK working with the energy source your dryer uses, nothing is stopping you.
I don't know which type dryer you have but luck of heat is a pretty common issue with any dryer (not just Maytag) and it has a number of causes - pretty much anything that has to do with heat generation, control and feedback can shut it off.
To sound less generic than that, I would need to know a bit more about your dryer - a model number is a great start - and the steps you've already taken to troubleshoot it. Simple things like reset the breaker to the circuit the dryer's on (both gas and electric). Does the drum light come on when you open the door, does control panel have lights or has it gone dark, any error codes flashing, any additional bit of info helps.
Also, this system lets you post pictures in case you need to illustrate something. Click on "+Image" button in the comment box to add pictures.