As dark_lord was explaining there is bassically 2 categories for laptops and their CPUs
The U serries laptops are designed for battery life and stay much cooler because they have lower powered CPUs in them. These laptops are great for everyday tasks, stay pretty cool and have good battery life. Now an i7 U serries is equiveleant to an i3 desktop cpu, they are a dusal core with 4 thread CPU with turbo core (usually bumping it up to around 2.8 ghz on demmand).
The HQ serries are more like their desktop counterparts (so an i7 is an actuall quad core + hyperthreading) and are designed for gaming or more demanding tasks, you can find these computers with dedicated grpahics and some with just the intel integrated graphics. These laptops are going to be thicker/heavier due to needing bigger batteries and cooling inside them and are despite that are still going to run hotter and use battery faster then the U serries.
So the first thing you need to decide if you need the performance of the HQ or not, as you are going to have the heat issue with the HQ no matter what.