Here's a good explanation:
Mazda 6 Club, Dr Wicked, 8 Feb 2004

Duratec Heated TB:

I've been lurking around here for a while, so here goes:

This is why it is a bad idea to bypass your throttle body coolant line:

First, we need to make some assumptions. The first set of these assumptions deals with the operating condition of the engine. Let’s assume that we are running the engine at full throttle at 4,000 RPM. We have a 3.0L engine that is efficient and has about an 85% volumetric efficiency. Our effective engine volume is 0.85*3.0L or 2.55L. Since we have a four stroke motor, we are pulling in 2.55L of air 2000 times a minute. Therefore we are ingesting 3.00 cubic feet of air per second, after unit conversions. Our throttle body’s inside diameter is 2.5 inches (D) and its total length is 2 inches (L).

The second set of assumptions deals with the air and coolant flowing through our throttle body. Let’s assume that we are pulling in air from outside the engine bay on a warm day. Our intake air is 80 degrees, Fahrenheit. At 80F and 1 atmosphere, air has the following properties:

Density (p): 0.0735 lbm/ft^3
Thermal conductivity (k): 0.01516 BTU/hr*ft*F
Kinematic Viscosity (v): 16.88*(10^-5) ft^2/s
Specific heat (Cp): 0.24 BTU/lbm*F
Prandtl Number (Pr): 0.708 Unitless

Let us also assume that our coolant is 280F and that our throttle body is not cooled significantly by the incoming air. That is, the surface temperature of the inside of the throttle body is always 280F.

Now we will figure out how much and how fast the air is entering the engine. Through simple calculations, knowing the throttle body dimensions and volumetric flow rate and the density of the air, we can find out the mass flow rate and velocity of the air entering the engine. These values are found to be 794 lbm/hr (m) and 88 ft/s (V).

We now need to know if the flow of the air is turbulent or laminar. This will allow us to determine what appropriate equations to use later. First, we need to find the Reynolds Number (a unitless number that allows one to know if the flow is turbulent or not). This is found by the equation:

Re = V*D/v

We find our Reynolds Number to be 110,000. This is definitely turbulent flow! (Anything over 10,000 is defined as fully turbulent flow)

We need to find our entry length, or the length of tubing needed for the flow to become fully turbulent. This value is defined as Lh = 10*D. This value is found to be 2.08 ft. This is acceptable, since there is, most likely, two feet of piping between the throttle body and the air filter.

Since our entry length is less than our actual piping length, we can use Dittus-Boulter equation to determine the Nusselt Number (Nu):. (Sorry about all of this name dropping)

Nu = 0.023*Re^.8*Pr^.4 = h*D/k

We find our Nusselt Number to be 214. The ‘h’ value above is the average heat transfer coefficient. Now, we can actually find the temperature of the air coming out of our throttle body. Solving for h in the above equation yields h equal to 15.58 BTU/hr*ft^2*F.

By using Newton’s law of cooling, where the rate of heat transfer (Q) is determined to be:

Q=h*(area of heat transfer)*(Surface temperature-Medium Temperature)

By using differential equations, natural logs and some other hocus pocus, we get the following equation:

Texit=Tsurface-(Tsurface-Tinlet)*exp(-h*A/m*Cp)

Finally, by using the above equation, the outlet temperature can be determined to be 81.3 degrees Fahrenheit.

Now, using the SAE J1349 correction factor, you lose ~1% of your total power for each 10 degree increase in inlet air temperature. With this 1.3 degree increase, due to the throttle body coolant, you are losing 0.13% of your power. Or, on a 200hp car, you are losing 0.26hp. By overriding the coolant flowing through your throttle body, you are risking having your throttle body freeze open in cold weather (the whole purpose of running coolant through the throttle body in the first place). Hope this clears up any confusion.

 

with engine temperatures under the hood being above freezing after car has warmed a couple minutes, how will the TB freeze? i have been running my Grand Marquis and Crown Vics with the EGR coolant lines bypassed. personally, it is also better than to find a coolant leak where engine sucks it in to the intake of the car due to a failed gasket on the EGR spacer.