Are you trying to measure heat flow or temperature?
What is the geometry? - are you measuring the flow of heat inside the material of the hollow block, or measuring the flow of heat from an object in the block, into the block itself?
What is the block made of?
Heat flow meters can be constructed from a pair of calibrated thermometers spaced apart by a material with well-described thermal properties. But without knowing the above, it is very hard to suggest how you might resolve this.
Also, knowing your desired accuracy and your available budget would help.