Fine-tuning pre-trained language models for downstream tasks has become a norm for NLP. Recently it is found that intermediate training can improve performance for fine-tuning language models for target tasks, high-level inference tasks such as Question Answering (QA) tend to work best as intermediate tasks. However it is not clear if intermediate training generally benefits various language models. In this paper, using the SQuAD-2.0 QA task for intermediate training for target text classification tasks, we experimented on eight tasks for single-sequence classification and eight tasks for sequence-pair classification using two base and two compact language models. Our experiments show that QA-based intermediate training generates varying transfer performance across different language models, except for similar QA tasks.