By default JMeter sends requests as fast as it can, the main factor which are affecting TPS rate are:
- number of threads (virtual users) - this you can define in Thread Group
- your application response time - this is not something you can control
Ideally when you increase number of threads the number of TPS should increase by the same factor, i.e. if you have 250 users and getting 100 tps you should get 200 tps for 500 users. If this is not the case - these 500 users are beyond saturation point and your application bottleneck is somewhere between 250 and 500 users (if not earlier).
With regards to "warm up" time - the recommended approach of conducting the load is doing it gradually, this way you will allow your application to get prepared to increasing load, warm up caches, let JIT compiler/optimizer to go their work, etc. Moreover this way you will be able to correlate the increasing load with increasing/decreasing throughput, response time, number of errors, etc. while having 250 users released at once doesn't tell the full story. See