Running a Peltier directly from a transistor
Yes - a transistor or MOSFET of an appropriate size and rating will easily control one or more Peltier cells. 

You are aware that a Peltier cell can both heat and cool simply by reversing the polarity of the DC voltage feeding the cell? 

If you give us more information regarding your setup, we can provide more information.

What is the voltage and current rating of your Peltier cells? 

What power supply voltage do you want to run from? 

FWIW - many Peltier coolers and heaters run from Automotive power supply nominal 12 Vdc.