A class A amplifier must be biased on at twice full power output into 8 ohms, or four times full power output into 4 ohms.  A 10 watt per channel class A amplifier that remains class A into 4 ohms will put out 40 watts of heat all the time from each channel, 80 watts total.  You might notice how hot a 100 watt light bulb gets.
68 degrees C is probably quite reasonable for a small class A amplifier.  However if you wanted 200 watts per channel class A, your amp would put out as much heat as a big home electric space heater. 

Not very "green".
Regards,
Frank Van Alstine