Why is burn feeling 'slower' than touch?
When you touch an object, a compression wave from the collision travels through your body at the speed of sound.  A sensor at any depth in your skin can pick up that signal at roughly the same time as the collision.

When you touch a hot object, heat from it moves into your body via conduction and to some extent radiation.  That heat flow moves much more slowly than the compression wave.  It will take longer for the heat pulse to reach a sensor that is deep in the skin and raise the temperature by a sufficient amount to cause signalling.  

There may be further differences in the sensory neurons or in the reaction to the signals.  But there is a physical reason for the temperature signals to lag touch signals from the same object.

"Thermoception and Temperature Regulation" edited by J. Bligh, K. Voigt has some discussion of a study of thermoreceptors in rabbits.  It suggests both that


signal latency increases with increasing depth in skin
while most receptors has short latency, some receptors had much greater latency, and that this disparity in response may aid in determining temperature gradients within the skin, not simply reading instantaneous skin temperature.