Ubuntu on my Laptop can now only suspend but not hibernate.
If I want to put the laptop into a bag and carry it to my class or office, will suspending it be okay? Will there be too much heat after the lid is closed?
This should not be a problem. When you put your computer to sleep, essentially only the RAM and a bit of circuitry to awake the laptop are left on. You'll notice that the fan also turns off because almost no heat is being generated once the CPU, GPU, and hard drive are turned off.
On Windows and OS X, the default behavior is usually to sleep the computer when the lid is closed. If it were unsafe to carry a laptop in a bag in sleep mode, this would not be the default.
This depends entirely on your notebook, and how the software you're running behaves. If some task sets the machine to wake-from-suspend while you have it in your bag, you're going to run the risk of overheating or hard-drive damage.
Hibernate is recommended when moving a machine around, Suspend when you're leaving the machine alone in one location for some time, and Sleep when walking away for a moment.