On an airliner, what is the temperature of the brakes after a typical landing, and how long does it take to cool down?
Is it hot enough that mechanics should wait before servicing an aircraft that has just touched down minutes before?
Judging by this IATA document, and looking at figure 4 in section 4.2.1, the brake temperature easily exceeds 700°C during landing. They also show some brake temperature history timeline for an airplane without fan cooling.
Managing Uneven Brake Temperatures on Twin-Aisle Airplanes During Short Flights was published by Boeing in 2001. The article details the threshold temperatures for the brake overheat warning of a few different twin-aisle plane types. Assuming that during a typical landing the brake overheat warning is not triggered and the brake system is not excessively over-designed, I would expect typical temperatures around 300 to 400 °C, very much depending on the plane.
The article also states that when leaving the gate, the brakes will still be warm from the previous landing, and that brake temperature may build up during the day. Note that (at least for the brakes shown) brake disks are not as exposed as the ones usually found in cars. Cooling through air flow seems quite limited.
Judging by that, I would say that yes, mechanics should be very careful before touching the brakes of a plane that has just landed. With the wheels mounted, we are talking more about hours, not minutes.
Steel brakes and carbon brakes have substantially different temperature ranges, and wear patterns.
Wear in steel brakes is accelerated substantially at higher temperatures, so (especially when taxiing) recommended brake usage is to use frequent, light applications of the brakes to maintain as close as possible to the preferred taxi speed. Most wear on steel brakes happens during landing, when you have little choice but to apply the brakes continuously, even though the temperature gets quite high.
With carbon brakes, rather the opposite is true: wear depends primarily on the number of times the brakes are applied, not the temperature reached. As such, the normal recommendation during taxiing is to let the speed run up to the maximum allowed, then apply the brakes fairly firmly and continuously once until the speed drops to a specified minimum. With carbon brakes, most wear (~75%) happens during taxiing. As already noted, wear depends primarily on the number of applications, not the temperature, and landing is typically just one application, even though it's a relatively protracted one that produces relatively high temperature.
For example, Boeing recommends as follows:
Because the wear mechanisms are different between carbon and steel brakes, different taxi braking techniques are recommended for carbon brakes in order to maximize brake life.
Steel brake wear is directly proportional to the kinetic energy absorbed by the brakes. Maximum steel brake life can be achieved during taxi by using a large number of small, light brake applications, allowing some time for brake cooling between applications. High airplane gross weights and high brake application speeds tend to reduce steel brake life because they require the brakes to absorb a large amount of kinetic energy.
Carbon brake wear is primarily dependent on the total number of brake applications — one firm brake application causes less wear than several light applications. Maximum carbon brake life can be achieved during taxi by using a small number of long, moderately firm brake applications instead of numerous light brake applications. This can be achieved by allowing taxi speed to increase from below target speed to above target speed, then using a single firm brake application to reduce speed below the target and repeating if required, rather than maintaining a constant taxi speed using numerous brake applications. Carbon brake wear is much less sensitive to airplane weight and speed than steel brake wear.
As such, it's perfectly normal for carbon brakes to operate at considerably higher temperatures than steel brakes. For carbon, typical operating range is about 600-800C. For Steel brakes, the preferred range is more like 400C. In both cases it also depends on what you measure--the temperature shown on the cockpit indicator is substantially below the peak temperature (at least in all cases of which I'm aware).
For what it's worth, steel brakes also cool faster than carbon brakes as a rule (though I haven't been able to find anything solid about exactly how much faster).
Here's a graph from Boeing showing the temperatures of the carbon brakes in a 777:
So yes, even an hour and a half after landing, the brakes are still hot enough that skin contact will result in a blister essentially immediately. As to waiting before servicing, that would depend on what servicing you're talking about doing. Refueling shortly after landing is common, and the brakes rarely affect its safety to any significant degree. Anything that involved removing the main landing gear wheels so the brakes were exposed...probably needs to wait quite a while longer. Other work near the brakes (e.g., servicing the struts) probably merits a little extra care right after landing, but there aren't too many cases where the brakes are likely to lead to a significant delay.