As you might know, you need the gas mass flow rate, its mean specific heat, hot gas temperature and ambient temperature. The problem would be in finding the mean specific heat as it depends on the composition of the exhaust gas.

Instead, you could set up a simple water-cooled heat exchanger of the double pipe type. Water flow rate and inlet/outlet temperatures are easily measured and the heat picked up calculated. You must also measure exhaust gas inlet/outlet temperatures. Then equate it to the heat lost by exhaust gas to calculate its heat capacity (mass flow rate times specific heat). But make sure the gas is well mixed after the heat exchanger when measuring its temperature. Insulate the whole heat exchanger well. Then the heat carried away can be easily calculated if you take the temperature difference (Tgas - Tambient). Do not cool the gas by more than, say, 100 C. This would be the simplest.

Then you can ignore errors in this method due to (i) the change of gas specific heat with temperature (ii) condensation of water vapor that might occur during cooling. It will give you a reasonable estimate.

Just a double pjpe heat exchanger

check the book name design of thermal system by stoeker for designing the heat exchanger simpler method