It matters a great deal what the characteristics of your relay are. There should be a specification for coil resistance that makes a great deal of difference as to how the circuit, and particularly the transistor will behave. It also matters what sort of MCU you are using and precisely how much current the port driving the base of the transistor can source.

Normally, one puts a resistor in the base simply to protect the base-emitter junction. However, it's a good idea to consider the entire circuit. The transistor is more than just a switch. The relay input circuit is more than just an inductor. The relay coil has a maximal voltage that it will drop at the rated current. It has a maximal current that it can tolerate, and it has a maximal current that it will pass at the rated voltage.

If you don't know these values, you can't properly design a circuit.

Additionally, there may not be a problem with the fact that the transistor gets "hot." Is it within its normal operating temperature range? How much current is it passing? Is it within the specified limits for your transistor?

RE