Sauna makes your heart work harder
Sauna definitely increases heart rate ([1] and [2])
Does sauna makes you burn calories the same as exercise ? No.
The most accurate method of measuring calorie burn is through VO2
testing
...
Combustion, which turns the fuel you receive from food into
energy, needs oxygen. Because there is a direct relationship between
how much oxygen you use and how much energy you burn, by measuring the
oxygen to carbon dioxide exchange through VO2 testing, you will get a
fairly precise gauge of how many calories you're burning.
eHow "How Heart Rate Monitors Calculate Calories Burned"
This study has show following results:
VO2 on exercise (ml/min) 1269,4 +/- 426,1
VO2 on suana (ml/min) 236,9 +/- 42,7
Oxygen update in suana was much less then during exercise.
What about sauna and sitting ?
Let's say sitting requires 1 MET, then for 120 kg person would intake about 120 ml / min.
Walking for the same person (120 kg) would be 120 kg * 3 ml / min kg = 360 ml / min
So, sauna makes your body burn more calories than sitting, it's can't be compared to exercises.